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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 5, Pages 1073–1107 (Mi izv1288)  

This article is cited in 27 scientific papers (total in 27 papers)

Operator invariants of tangles, and $R$-matrices

V. G. Turaev


Abstract: Operator invariant of tangles are introduced. They generalize both representations of braid groups involving $R$-matrices and the recently introduced Jones–Conway and Kauffman polynomials of links.
Bibliography: 25 titles.

Full text: PDF file (4052 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1990, 35:2, 411–444

Bibliographic databases:

UDC: 515.162.8
MSC: Primary 57M25; Secondary 57M05, 81E99
Received: 03.03.1988

Citation: V. G. Turaev, “Operator invariants of tangles, and $R$-matrices”, Izv. Akad. Nauk SSSR Ser. Mat., 53:5 (1989), 1073–1107; Math. USSR-Izv., 35:2 (1990), 411–444

Citation in format AMSBIB
\Bibitem{Tur89}
\by V.~G.~Turaev
\paper Operator invariants of tangles, and $R$-matrices
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 5
\pages 1073--1107
\mathnet{http://mi.mathnet.ru/izv1288}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1024455}
\zmath{https://zbmath.org/?q=an:0707.57003}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 35
\issue 2
\pages 411--444
\crossref{https://doi.org/10.1070/IM1990v035n02ABEH000711}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. J C Baez, Class Quantum Grav, 10:4 (1993), 673  crossref  mathscinet  zmath  adsnasa
    2. Tetsuo Deguchi, Kyoichi Tsurusaki, “A new algorithm for numerical calculation of link invariants”, Physics Letters A, 174:1-2 (1993), 29  crossref
    3. John C. Baez, James Dolan, “Higher-dimensional algebra and topological quantum field theory”, J Math Phys (N Y ), 36:11 (1995), 6073  crossref  mathscinet  zmath
    4. Sergey Piunikhin, “Combinatorial expression for universal Vassiliev link invariant”, Comm Math Phys, 168:1 (1995), 1  crossref  mathscinet  zmath
    5. Tu Quoc Thang Le, Jun Murakami, “Representation of the category of tangles by Kontsevich's iterated integral”, Comm Math Phys, 168:3 (1995), 535  crossref  mathscinet  zmath
    6. H C Lee, J Phys A Math Gen, 29:2 (1996), 393  crossref  zmath  adsnasa
    7. Tammo Dieck, “On tensor representations of knot algebras”, manuscripta math, 93:1 (1997), 163  crossref  mathscinet  zmath  isi
    8. J.Scott Carter, Joachim H. Rieger, Masahico Saito, “A Combinatorial Description of Knotted Surfaces and Their Isotopies”, Advances in Mathematics, 127:1 (1997), 1  crossref
    9. John C. Baez, “Higher-Dimensional Algebra II. 2-Hilbert Spaces”, Advances in Mathematics, 127:2 (1997), 125  crossref
    10. Roger Picken, “Reflections on topological quantum field theory”, Reports on Mathematical Physics, 40:2 (1997), 295  crossref
    11. I. A. Dynnikov, “Three-Page Approach to Knot Theory. Encoding and Local Moves”, Funct. Anal. Appl., 33:4 (1999), 260–269  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. Masashi Kosuda, “The Irreducible Representations of the Hecke Category”, Journal of Algebra, 215:1 (1999), 135  crossref
    13. I. A. Dynnikov, “Three-Page Approach to Knot Theory. Universal Semigroup”, Funct. Anal. Appl., 34:1 (2000), 24–32  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. I. A. Dynnikov, “Finitely Presented Groups and Semigroups in Knot Theory”, Proc. Steklov Inst. Math., 231 (2000), 220–237  mathnet  mathscinet  zmath
    15. Miyuki K. Shimamura, Tetsuo Deguchi, “Characteristic length of random knotting for cylindrical self-avoiding polygons”, Physics Letters A, 274:5-6 (2000), 184  crossref  elib
    16. Miyuki K. Shimamura, Tetsuo Deguchi, “Gyration radius of a circular polymer under a topological constraint with excluded volume”, Phys Rev E, 64:2 (2001), 020801  crossref
    17. Miyuki K. Shimamura, Tetsuo Deguchi, “Topological Entropy of a Stiff Ring Polymer and Its Connection to DNA Knots”, J Phys Soc Jpn, 70:6 (2001), 1523  crossref  isi
    18. Miyuki K Shimamura, Tetsuo Deguchi, “Anomalous finite-size effects for the mean-squared gyration radius of Gaussian random knots”, J Phys A Math Gen, 35:18 (2002), L241  crossref  mathscinet  zmath
    19. Fumikazu NAGASATO, “A Diagrammatic Construction of the (sl(N,C),ρ)-Weight System”, Iis, 9:1 (2003), 43  crossref  mathscinet  zmath
    20. John C. Baez, Laurel Langford, “Higher-dimensional algebra IV: 2-tangles”, Advances in Mathematics, 180:2 (2003), 705  crossref
    21. V. V. Vershinin, V. A. Kurlin, “Three-Page Embeddings of Singular Knots”, Funct. Anal. Appl., 38:1 (2004), 14–27  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    22. P. P. Nikitin, “Representation theory and the branching graph for the family of Turaev algebras”, J. Math. Sci. (N. Y.), 138:3 (2006), 5727–5732  mathnet  crossref  mathscinet  zmath  elib  elib
    23. A. M. Vershik, P. P. Nikitin, “Traces on Infinite-Dimensional Brauer Algebras”, Funct. Anal. Appl., 40:3 (2006), 165–172  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    24. P. P. Nikitin, “The centralizer algebra of the diagonal action of the group $GL_n(\mathbb C)$ in a mixed tensor space”, J. Math. Sci. (N. Y.), 141:4 (2007), 1479–1493  mathnet  crossref  mathscinet  zmath  elib  elib
    25. Donald Yau, “The Hom–Yang–Baxter equation and Hom–Lie algebras”, J. Math. Phys, 52:5 (2011), 053502  crossref
    26. Carmen Caprau, Joel Smith, “The Singular Temperley-Lieb Category”, ISRN Geometry, 2014 (2014), 1  crossref
    27. C. Lescop, “An introduction to finite type invariants of knots and 3-manifolds defined by counting graph configurations”, Vestnik ChelGU, 2015, no. 17, 67–117  mathnet
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