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TMF, 1999, Volume 120, Number 3, Pages 511–528 (Mi tmf793)  

This article is cited in 127 scientific papers (total in 127 papers)

A quantum Teichmüller space

V. V. Focka, L. O. Chekhovb

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We explicitly describe a noncommutative deformation of the $*$-algebra of functions on the Teichmüller space of Riemann surfaces with holes that is equivariant with respect to the action of the mapping class group.

DOI: https://doi.org/10.4213/tmf793

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English version:
Theoretical and Mathematical Physics, 1999, 120:3, 1245–1259

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Received: 24.05.1999

Citation: V. V. Fock, L. O. Chekhov, “A quantum Teichmüller space”, TMF, 120:3 (1999), 511–528; Theoret. and Math. Phys., 120:3 (1999), 1245–1259

Citation in format AMSBIB
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\paper A quantum Teichm\"uller space
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\transl
\jour Theoret. and Math. Phys.
\yr 1999
\vol 120
\issue 3
\pages 1245--1259
\crossref{https://doi.org/10.1007/BF02557246}
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    1. Bertola M. Korotkin D., “Hodge and Prym Tau Functions, Strebel Differentials and Combinatorial Model of Mg, N”, Commun. Math. Phys.  crossref  isi
    2. Coman I., Pomoni E., Teschner J., “Toda Conformal Blocks, Quantum Groups, and Flat Connections”, Commun. Math. Phys.  crossref  isi
    3. L. O. Chekhov, “A spectral problem on graphs and $L$-functions”, Russian Math. Surveys, 54:6 (1999), 1197–1232  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. Chekhov, LO, “Observables in 3D gravity and geodesic algebras”, Czechoslovak Journal of Physics, 50:11 (2000), 1201  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    5. L. O. Chekhov, “Observables in $2+1$ Gravity and Noncommutative Teichmüller Spaces”, Theoret. and Math. Phys., 129:2 (2001), 1609–1616  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Hikami, K, “Hyperbolicity of partition function and quantum gravity”, Nuclear Physics B, 616:3 (2001), 537  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    7. Hikami, K, “Hyperbolic structure arising from a knot invariant”, International Journal of Modern Physics A, 16:19 (2001), 3309  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    8. Hikami, K, “The Baxter equation for quantum discrete Boussinesq equation”, Nuclear Physics B, 604:3 (2001), 580  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    9. Phys. Usp., 44:4 (2001), 424–427  mathnet  crossref  crossref  isi
    10. Kashaev R., “The quantum dilogarithm and Dehn twists in quantum Teichmüller theory”, Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 35, 2001, 211–221  mathscinet  zmath  isi
    11. Kashaev R.M., “On the spectrum of Dehn twists in quantum Teichmüller theory”, Physics and Combinatorics, 2001, 63–81  crossref  mathscinet  zmath  adsnasa  isi
    12. Krasnov, K, “Lambda < 0 quantum gravity in 2+1 dimensions: I. Quantum states and stringy S-matrix”, Classical and Quantum Gravity, 19:15 (2002), 3977  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    13. Hikami, K, “Hyperbolic structure arising from a knot invariant II: Completeness”, International Journal of Modern Physics B, 16:14–15 (2002), 1963  crossref  mathscinet  zmath  adsnasa  isi
    14. Faddeev, LD, “Strongly coupled quantum discrete Liouville theory: II. Geometric interpretation of the evolution operator”, Journal of Physics A-Mathematical and General, 35:18 (2002), 4043  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    15. L. O. Chekhov, R. C. Penner, “Introduction to quantum Thurston theory”, Russian Math. Surveys, 58:6 (2003), 1141–1183  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    16. Krasnov, K, “On holomorphic factorization in asymptotically AdS 3D gravity”, Classical and Quantum Gravity, 20:18 (2003), 4015  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    17. Teschner, J, “Quantum Liouville theory versus quantized Teichmüller spaces”, Fortschritte der Physik-Progress of Physics, 51:7–8 (2003), 865  crossref  mathscinet  zmath  isi
    18. Nazarenko, AV, “Quantization of reduced Chern–Simons gravity with a source”, International Journal of Modern Physics A, 19:28 (2004), 4883  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    19. Freidel, L, “2D conformal field theories and holography”, Journal of Mathematical Physics, 45:6 (2004), 2378  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    20. Teschner J., “On the relation between quantum Liouville theory and the quantized Teichmüller spaces”, International Journal of Modern Physics A, 19 (2004), 459–477, Suppl. S  crossref  mathscinet  zmath  adsnasa  isi
    21. R. M. Kashaev, “On selfadjont extensions of a difference operator”, St. Petersburg Math. J., 17:1 (2006), 157–167  mathnet  crossref  mathscinet  zmath
    22. Nazarenko, A, “Time level splitting in quantum Chern–Simons gravity”, Classical and Quantum Gravity, 22:11 (2005), 2107  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    23. Kashaev, RM, “Coordinates for the moduli space of flat PSL(2, R)-connections”, Mathematical Research Letters, 12:1 (2005), 23  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    24. Chekhov, L, “Extension of geodesic algebras to continuous genus”, Letters in Mathematical Physics, 78:1 (2006), 17  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    25. Bai, H, “Quantum Teichmuller spaces and Kashaev's 6j-symbols”, Algebraic and Geometric Topology, 7 (2007), 1541  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    26. Bonahon, F, “Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms”, Geometry & Topology, 11 (2007), 889  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    27. Bai, H, “A uniqueness property for the quantization of Teichmüller Spaces”, Geometriae Dedicata, 128:1 (2007), 1  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    28. Andersson, L, “Notes on a paper of Mess”, Geometriae Dedicata, 126:1 (2007), 47  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    29. Hikami, K, “Generalized volume conjecture and the A-polynomials: The Neumann-Zagier potential function as a classical limit of the partition function”, Journal of Geometry and Physics, 57:9 (2007), 1895  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    30. Leonid O. Chekhov, “Teichmüller Theory of Bordered Surfaces”, SIGMA, 3 (2007), 066, 37 pp.  mathnet  crossref  mathscinet  zmath
    31. Teschner J., “From Liouville theory to the quantum geometry of Riemann surfaces”, Prospects in Mathematical Physics, Contemporary Mathematics Series, 437, 2007, 231–246  crossref  mathscinet  zmath  isi
    32. L. D. Faddeev, “Discrete Series of Representations for the Modular Double of the Quantum Group $U_q(\operatorname{sl}(2,\mathbb{R}))$”, Funct. Anal. Appl., 42:4 (2008), 330–335  mathnet  crossref  crossref  mathscinet  zmath  isi
    33. Papadopoulos, A, “Shift coordinates, stretch lines and polyhedral structures for Teichmüller space”, Monatshefte fur Mathematik, 153:4 (2008), 309  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    34. Penner, RC, “Teichmüller theory of the punctured solenoid”, Geometriae Dedicata, 132:1 (2008), 179  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    35. Bazhanov, VV, “Quantum geometry of three-dimensional lattices”, Journal of Statistical Mechanics-Theory and Experiment, 2008, P07004  crossref  mathscinet  isi  scopus  scopus
    36. L. O. Chekhov, “Riemann Surfaces with Orbifold Points”, Proc. Steklov Inst. Math., 266 (2009), 228–250  mathnet  crossref  mathscinet  zmath  isi  elib  elib
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    38. Gorsky, A, “Amplitudes in the N=4 supersymmetric Yang-Mills theory from quantum geometry of momentum space”, Physical Review D, 80:12 (2009), 125002  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus  scopus
    39. Chekhov, LO, “Orbifold Riemann surfaces and geodesic algebras”, Journal of Physics A-Mathematical and Theoretical, 42:30 (2009), 304007  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
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    47. Nekrasov N., Witten E., “The omega deformation, branes, integrability and Liouville theory”, Journal of High Energy Physics, 2010, no. 9, 092  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
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    50. A. V. Marshakov, “Gauge theories as matrix models”, Theoret. and Math. Phys., 169:3 (2011), 1704–1723  mathnet  crossref  crossref  mathscinet  isi
    51. Harlow D., Maltz J., Witten E., “Analytic continuation of Liouville theory”, Journal of High Energy Physics, 2011, no. 12, 071  crossref  mathscinet  zmath  isi  scopus  scopus
    52. Nekrasov N., Rosly A., Shatashvili S., “Darboux coordinates, Yang-Yang functional, and gauge theory”, Nuclear Phys B Proc Suppl, 216 (2011), 69–93  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
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    55. Bonahon F., Wong H., “Quantum traces for representations of surface groups in SL2(C)”, Geometry & Topology, 15:3 (2011), 1569–1615  crossref  mathscinet  zmath  isi  scopus  scopus
    56. Neretin Yu.A., “Double Cosets for SU(2) x ... x SU(2) and Outer Automorphisms of Free Groups”, Int Math Res Not, 2011, no. 9, 2047–2067  mathscinet  zmath  isi  elib
    57. Chekhov L., Mazzocco M., “Isomonodromic deformations and twisted Yangians arising in Teichmüller theory”, Adv Math, 226:6 (2011), 4731–4775  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    58. Bonsante F., Krasnov K., Schlenker J.-M., “Multi-black Holes and Earthquakes on Riemann Surfaces with Boundaries”, Int Math Res Not, 2011, no. 3, 487–552  mathscinet  zmath  isi
    59. Makover E., McGowan J., “The length of closed geodesics on random Riemann surfaces”, Geom Dedicata, 151:1 (2011), 207–220  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    60. Teschner J., “Quantization of the Hitchin Moduli Spaces, Liouville Theory and the Geometric Langlands Correspondence I”, Adv. Theor. Math. Phys., 15:2 (2011), 471–564  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    61. Bonahon F., Wong H., “Kauffman Brackets, Character Varieties and Triangulations of Surfaces”, Topology and Geometry in Dimension Three: Triangulations, Invariants, and Geometric Structures, Contemporary Mathematics, 560, eds. Li W., Bartolini L., Johnson J., Luo F., Myers R., Rubinstein J., Amer Mathematical Soc, 2011, 179–194  crossref  mathscinet  zmath  isi
    62. Frenkel I.B., Kim H.K., “Quantum Teichmüller Space From the Quantum Plane”, Duke Math J, 161:2 (2012), 305–366  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    63. Chekhov L., Mazzocco M., “Teichmüller Spaces as Degenerated Symplectic Leaves in Dubrovin-Ugaglia Poisson Manifolds”, Physica D, 241:23-24 (2012), 2109–2121  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    64. A. Yu. Vasiliev, A. G. Sergeev, “Classical and quantum Teichmüller spaces”, Russian Math. Surveys, 68:3 (2013), 435–502  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    65. Zarrinkamar S., Hassanabadi H., Rajabi A.A., “On Multi-Point Liouville Field Theory”, Few-Body Syst., 54:11 (2013), 1997–1999  crossref  adsnasa  isi  elib  scopus  scopus
    66. Dimofte T., Gukov S., “Chern–Simons Theory and S-Duality”, J. High Energy Phys., 2013, no. 5, 109  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    67. Ip I.C.H., “The Classical Limit of Representation Theory of the Quantum Plane”, Int. J. Math., 24:4 (2013), 1350031  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    68. Luo F., “Volume Optimization, Normal Surfaces, and Thurston's Equation on Triangulated 3-Manifolds”, J. Differ. Geom., 93:2 (2013), 299–326  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    69. Ip I.Ch.-H., “Representation of the Quantum Plane, its Quantum Double, and Harmonic Analysis on”, Sel. Math.-New Ser., 19:4 (2013), 987–1082  crossref  mathscinet  zmath  isi  scopus  scopus
    70. Roger J., “Factorization Rules in Quantum Teichmüller Theory”, Algebr. Geom. Topol., 13:6 (2013), 3411–3446  crossref  mathscinet  zmath  isi  scopus  scopus
    71. Dimofte T., Garoufalidis S., “The Quantum Content of the Gluing Equations”, Geom. Topol., 17:3 (2013), 1253–1315  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    72. Gang D., Koh E., Lee S., Park J., “Superconformal Index and 3D-3D Correspondence for Mapping Cylinder/Torus”, J. High Energy Phys., 2014, no. 1, 063  crossref  isi  scopus  scopus
    73. Dimofte T., Gaiotto D., Gukov S., “Gauge Theories Labelled by Three-Manifolds”, Commun. Math. Phys., 325:2 (2014), 367–419  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    74. L. D. Faddeev, “Zero Modes for the Quantum Liouville Model”, Funct. Anal. Appl., 48:3 (2014), 166–174  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    75. N. A. Nekrasov, A. A. Roslyi, S. L. Shatashvili, “Darboux coordinates, Yang–Yang functional, and gauge theory”, Theoret. and Math. Phys., 181:1 (2014), 1206–1234  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    76. Andersen J.E., Kashaev R., “A TQFT From Quantum Teichmüller Theory”, Commun. Math. Phys., 330:3 (2014), 887–934  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    77. Terashima Yu., Yamazaki M., “N=2 Theories From Cluster Algebras”, Prog. Theor. Exp. Phys., 2014, no. 2, 023B01  crossref  zmath  isi  scopus  scopus
    78. Andersen J.E., Kashaev R.M., “Quantum Teichmüller Theory and TQFT”, Xviith International Congress on Mathematical Physics, ed. Jensen A., World Scientific Publ Co Pte Ltd, 2014, 684–692  mathscinet  zmath  isi
    79. Chekhov L., Shapiro M., “Teichmüller Spaces of Riemann Surfaces With Orbifold Points of Arbitrary Order and Cluster Variables”, Int. Math. Res. Notices, 2014, no. 10, 2746–2772  crossref  mathscinet  zmath  isi  scopus  scopus
    80. Frenkel I.B., Ip I.C.H., “Positive Representations of Split Real Quantum Groups and Future Perspectives”, Int. Math. Res. Notices, 2014, no. 8, 2126–2164  crossref  mathscinet  zmath  isi  scopus  scopus
    81. Roger J., Yang T., “The Skein Algebra of Arcs and Links and the Decorated Teichmüller Space”, J. Differ. Geom., 96:1 (2014), 95–140  crossref  mathscinet  zmath  isi  scopus  scopus
    82. Luo F., “Rigidity of Polyhedral Surfaces, i”, J. Differ. Geom., 96:2 (2014), 241–302  crossref  mathscinet  zmath  isi  scopus  scopus
    83. L. A. Takhtadzhyan, L. D. Faddeev, “The spectral theory of a functional-difference operator in conformal field theory”, Izv. Math., 79:2 (2015), 388–410  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    84. Teschner J., Vartanov G.S., “Supersymmetric Gauge Theories, Quantization of M-Flat, and Conformal Field Theory”, Adv. Theor. Math. Phys., 19:1 (2015), 1–135  crossref  mathscinet  zmath  isi  scopus  scopus
    85. Dimofte T., Gaiotto D., van der Veen R., “Rg Domain Walls and Hybrid Triangulations”, Adv. Theor. Math. Phys., 19:1 (2015), 137–276  crossref  mathscinet  zmath  isi  scopus  scopus
    86. Wolpert S.A., “Products of Twists, Geodesic Lengths and Thurston Shears”, Compos. Math., 151:2 (2015), 313–350  crossref  mathscinet  zmath  isi  scopus  scopus
    87. Jackson S., McGough L., Verlinde H., “Conformal Bootstrap, Universality and Gravitational Scattering”, Nucl. Phys. B, 901 (2015), 382–429  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    88. Kim J., Porrati M., “on a Canonical Quantization of 3D Anti de Sitter Pure Gravity”, J. High Energy Phys., 2015, no. 10, 096  crossref  mathscinet  isi  scopus  scopus
    89. Xu B., “Central extension of mapping class group via Chekhov?Fock quantization”, J. Geom. Phys., 110 (2016), 9–24  crossref  mathscinet  isi  elib  scopus
    90. Kashaev R., Marino M., “Operators from Mirror Curves and the Quantum Dilogarithm”, Commun. Math. Phys., 346:3 (2016), 967–994  crossref  mathscinet  zmath  isi  elib  scopus
    91. Alexandrov S., Pioline B., “Theta Series, Wall-Crossing and Quantum Dilogarithm Identities”, Lett. Math. Phys., 106:8 (2016), 1037–1066  crossref  mathscinet  zmath  isi  scopus
    92. Meusburger C., Scarinci C., “Generalized shear coordinates on the moduli spaces of three-dimensional spacetimes”, J. Differ. Geom., 103:3 (2016), 425–474  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    93. Kim H.K., “Ratio coordinates for higher Teichmüller spaces”, Math. Z., 283:1-2 (2016), 469–513  crossref  mathscinet  zmath  isi  elib  scopus
    94. Kashaev R., Luo F., Vartanov G., “A TQFT of Turaev–Viro Type on Shaped Triangulations”, Ann. Henri Poincare, 17:5 (2016), 1109–1143  crossref  mathscinet  zmath  isi  elib  scopus
    95. Kim H.K., “The dilogarithmic central extension of the Ptolemy?Thompson group via the Kashaev quantization”, Adv. Math., 293 (2016), 529–588  crossref  mathscinet  zmath  isi  elib  scopus
    96. Bonahon F., Wong H., “Representations of the Kauffman bracket skein algebra I: invariants and miraculous cancellations”, Invent. Math., 204:1 (2016), 195–243  crossref  mathscinet  zmath  isi  elib  scopus
    97. Muller G., “Skein and cluster algebras of marked surfaces”, Quantum Topol., 7:3 (2016), 435–503  crossref  mathscinet  zmath  isi  elib  scopus
    98. Dimofte T., Gabella M., Goncharov A.B., “K-Decompositions and 3D Gauge Theories”, J. High Energy Phys., 2016, no. 11, 151  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    99. Gabella M., “Quantum Holonomies from Spectral Networks and Framed BPS States”, Commun. Math. Phys., 351:2 (2017), 563–598  crossref  mathscinet  zmath  isi  scopus
    100. Han M., “Sl(2,C) Chern–Simons Theory and Four-Dimensional Quantum Geometry”, String-Math 2015, Proceedings of Symposia in Pure Mathematics, 96, eds. Li S., Lian B., Song W., Yau S., Amer Mathematical Soc, 2017, 141–155  crossref  mathscinet  isi  scopus  scopus
    101. Chekhov L.O., Mazzocco M., Rubtsov V.N., “Painlevé Monodromy Manifolds, Decorated Character Varieties, and Cluster Algebras”, Int. Math. Res. Notices, 2017, no. 24, 7639–7691  crossref  mathscinet  isi
    102. Bonahon F., Wong H., “Representations of the Kauffman Bracket Skein Algebra II: Punctured Surfaces”, Algebr. Geom. Topol., 17:6 (2017), 3399–3434  crossref  mathscinet  zmath  isi  scopus  scopus
    103. Dimofte T., “Perturbative and Nonperturbative Aspects of Complex Chern–Simons Theory”, J. Phys. A-Math. Theor., 50:44 (2017), 443009  crossref  mathscinet  zmath  isi  scopus  scopus
    104. Aghaei N., Pawelkiewicz M., Teschner J., “Quantisation of Super Teichmüller Theory”, Commun. Math. Phys., 353:2 (2017), 597–631  crossref  mathscinet  zmath  isi  scopus  scopus
    105. Chekhov L., Mazzocco M., “Colliding Holes in Riemann Surfaces and Quantum Cluster Algebras”, Nonlinearity, 31:1 (2018), 54–107  crossref  mathscinet  zmath  isi  scopus  scopus
    106. Yamazaki M., “Quantum Trilogy: Discrete Toda, Y-System and Chaos”, J. Phys. A-Math. Theor., 51:5 (2018), 053002  crossref  mathscinet  zmath  isi  scopus  scopus
    107. Toulisse J., “Irreducible Decomposition For Local Representations of Quantum Teichmüller Space”, Pac. J. Math., 294:1 (2018), 233–256  crossref  mathscinet  zmath  isi  scopus  scopus
    108. Ip I.C.H., “On Tensor Products of Positive Representations of Split Real Quantum Borel Subalgebra Uq(Q)Over-Tilde(B(R))”, Trans. Am. Math. Soc., 370:6 (2018), 4177–4200  crossref  mathscinet  zmath  isi  scopus  scopus
    109. Mikhaylov V., “Teichmüller TQFT Vs. Chern–Simons Theory”, J. High Energy Phys., 2018, no. 4, 085  crossref  mathscinet  isi  scopus  scopus
    110. Le T.T.Q., “On Positivity of Kauffman Bracket Skein Algebras of Surfaces”, Int. Math. Res. Notices, 2018, no. 5, 1314–1328  crossref  mathscinet  isi
    111. Le T.T.Q., “Triangular Decomposition of Skein Algebras”, Quantum Topol., 9:3 (2018), 591–632  crossref  mathscinet  zmath  isi  scopus
    112. Mazzocco M., “Embedding of the Rank 1 Daha Into Mat(2, T-Q) and Its Automorphisms”, Representation Theory, Special Functions and Painleve Equations - Rims 2015, Advanced Studies in Pure Mathematics, 76, eds. Konno H., Sakai H., Shiraishi J., Suzuki T., Yamada Y., Math Soc Japan, 2018, 449–468  mathscinet  isi
    113. Nakanishi T., “Rogers Dilogarithms of Higher Degree and Generalized Cluster Algebras”, J. Math. Soc. Jpn., 70:4 (2018), 1269–1304  crossref  mathscinet  zmath  isi  scopus
    114. Kazuhiro Hikami, “Note on Character Varieties and Cluster Algebras”, SIGMA, 15 (2019), 003, 32 pp.  mathnet  crossref
    115. Kim H.K., “Finite Dimensional Quantum Teichmuller Space From the Quantum Torus At Root of Unity”, J. Pure Appl. Algebr., 223:3 (2019), 1337–1381  crossref  mathscinet  zmath  isi  scopus
    116. Przytycki J.H., Sikora A.S., “Skein Algebras of Surfaces”, Trans. Am. Math. Soc., 371:2 (2019), 1309–1332  crossref  mathscinet  zmath  isi  scopus
    117. Frohman Ch., Kania-Bartoszynska J., Le T., “Unicity For Representations of the Kauffman Bracket Skein Algebra”, Invent. Math., 215:2 (2019), 609–650  crossref  mathscinet  zmath  isi  scopus
    118. Penner R.C., Zeitlin A.M., “Decorated Super-Teichmuller Space”, J. Differ. Geom., 111:3 (2019), 527–566  crossref  mathscinet  zmath  isi
    119. Le T.T.Q., “Quantum Teichmuller Spaces and Quantum Trace Map”, J. Inst. Math. Jussieu, 18:2 (2019), 249–291  crossref  mathscinet  zmath  isi  scopus
    120. Bonahon F., Wong H., “Representations of the Kauffman Bracket Skein Algebra III: Closed Surfaces and Naturality”, Quantum Topol., 10:2 (2019), 325–398  crossref  mathscinet  isi
    121. A. B. Bogatyrev, “Combinatorial analysis of the period mapping: the topology of 2D fibres”, Sb. Math., 210:11 (2019), 1531–1562  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    122. Haggard H.M., Han M., Kaminski W., Riello A., “Sl(2,C) Chern-Simons Theory, Flat Connections, and Four-Dimensional Quantum Geometry”, Adv. Theor. Math. Phys., 23:4 (2019), 1067–1158  isi
    123. Leonid O. Chekhov, “Symplectic Structures on Teichmüller Spaces $\mathfrak T_{g,s,n}$ and Cluster Algebras”, Proc. Steklov Inst. Math., 309 (2020), 87–96  mathnet  crossref  crossref  isi  elib
    124. L. O. Chekhov, “Fenchel–Nielsen coordinates and Goldman brackets”, Russian Math. Surveys, 75:5 (2020), 929–964  mathnet  crossref  crossref  mathscinet  isi  elib
    125. Cho S.Y., Kim H., Kim H.K., Oh D., “Laurent Positivity of Quantized Canonical Bases For Quantum Cluster Varieties From Surfaces”, Commun. Math. Phys., 373:2 (2020), 655–705  crossref  isi
    126. Bossinger L., Frias-Medina B., Magee T., Najera Chavez A., “Toric Degenerations of Cluster Varieties and Cluster Duality”, Compos. Math., 156:10 (2020), 2149–2206  crossref  isi
    127. Morier-Genoud S., Ovsienko V., “Q-Deformed Rationals and Q-Continued Fractions”, Forum Math. Sigma, 8 (2020), e13  crossref  isi
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