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Uspekhi Mat. Nauk, 1999, Volume 54, Issue 1(325), Pages 213–250 (Mi umn122)  

This article is cited in 30 scientific papers (total in 30 papers)

Wess–Zumino–Witten–Novikov theory, Knizhnik–Zamolodchikov equations, and Krichever–Novikov algebras

M. Schlichenmaiera, O. K. Sheinmanb

a University of Mannheim
b Independent University of Moscow

DOI: https://doi.org/10.4213/rm122

Full text: PDF file (459 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1999, 54:1, 213–249

Bibliographic databases:

UDC: 517.774
MSC: 17B66, 17B67, 14H10, 14H15, 17B90, 30F30, 14H55, 81R10, 81T40
Received: 15.12.1998

Citation: M. Schlichenmaier, O. K. Sheinman, “Wess–Zumino–Witten–Novikov theory, Knizhnik–Zamolodchikov equations, and Krichever–Novikov algebras”, Uspekhi Mat. Nauk, 54:1(325) (1999), 213–250; Russian Math. Surveys, 54:1 (1999), 213–249

Citation in format AMSBIB
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\pages 213--250
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    This publication is cited in the following articles:
    1. O. K. Sheinman, “The Fermion Model of Representations of Affine Krichever–Novikov Algebras”, Funct. Anal. Appl., 35:3 (2001), 209–219  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. O. K. Sheinman, “Second order Casimirs for the affine Krichever–Novikov algebras $\widehat{\mathfrak{gl}}_{g,2}$ and $\widehat{\mathfrak{sl}}_{g,2}$”, Mosc. Math. J., 1:4 (2001), 605–628  mathnet  mathscinet  zmath
    3. Skrypnyk, T, “Quasigraded Lie algebras on hyperelliptic curves and classical integrable systems”, Journal of Mathematical Physics, 42:9 (2001), 4570  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. Wagemann, F, “Explicit formulae for cocycles of holomorphic vector fields with values in gimel densities”, Journal of Lie Theory, 11:1 (2001), 173  mathscinet  zmath  isi
    5. M. Schlichenmaier, “Higher genus affine algebras of Krichever–Novikov type”, Mosc. Math. J., 3:4 (2003), 1395–1427  mathnet  mathscinet  zmath
    6. Fialowski A., Schlichenmaier M., “Global deformations of the Witt algebra of Krichever-Novikov type”, Commun. Contemp. Math., 5:6 (2003), 921–945  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Schlichenmaier M., “Local cocycles and central extensions for multipoint algebras of Krichever-Novikov type”, J. Reine Angew. Math., 559 (2003), 53–94  crossref  mathscinet  zmath  isi
    8. M. Schlichenmaier, O. K. Sheinman, “Knizhnik–Zamolodchikov equations for positive genus and Krichever–Novikov algebras”, Russian Math. Surveys, 59:4 (2004), 737–770  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. O. K. Sheinman, “Projective Flat Connections on Moduli Spaces of Riemann Surfaces and the Knizhnik–Zamolodchikov Equations”, Proc. Steklov Inst. Math., 251 (2005), 293–304  mathnet  mathscinet  zmath
    10. Fialowski, A, “Global geometric deformations of current algebras as Krichever-Novikov type algebras”, Communications in Mathematical Physics, 260:3 (2005), 579  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    11. Sheinman O.K., “Krichever-Novikov algebras and their representations”, Noncommutative Geometry and Representation Theory in Mathematical Physics, Contemporary Mathematics Series, 391, 2005, 313–321  crossref  mathscinet  zmath  isi
    12. A. Fialowski, M. Schlichenmaier, “Global Geometric Deformations of the Virasoro Algebra, Current and Affine Algebras by Krichever–Novikov Type Algebras”, Int J Theor Phys, 46:11 (2007), 2708  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    13. O. K. Sheinman, “Krichever–Novikov Algebras, their Representations and Applications in Geometry and Mathematical Physics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S85–S161  mathnet  crossref  crossref  zmath
    14. Schlichenmaier M., “Higher Genus Affine Lie Algebras of Krichever - Novikov Type”, Difference Equations, Special Functions and Orthogonal Polynomials, 2007, 589–599  crossref  mathscinet  zmath  isi
    15. Schlichenmaier M., “A global operator approach to Wess-Zumino-Novikov-Witten models”, XXVI Workshop on Geometrical Methods in Physics, AIP Conference Proceedings, 956, 2007, 107–119  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    16. M. Schlichenmaier, O. K. Sheinman, “Central extensions of Lax operator algebras”, Russian Math. Surveys, 63:4 (2008), 727–766  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    17. Schlichenmaier M., “Classification of central extensions of Lax operator algebras”, Geometric Methods in Physics, AIP Conference Proceedings, 1079, 2008, 227–234  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    18. Schlichenmaier M., “Deformations of the Witt, Virasoro, and Current Algebra”, Generalized Lie Theory in Mathematics, Physics and Beyond, 2009, 219–234  crossref  mathscinet  zmath  isi  scopus  scopus
    19. Cox B., Futorny V., “DJKM Algebras I: their Universal Central Extension”, Proc Amer Math Soc, 139:10 (2011), 3451–3460  crossref  mathscinet  zmath  isi  scopus  scopus
    20. MARTIN SCHLICHENMAIER, “KRICHEVER-NOVIKOV TYPE ALGEBRAS — PERSONAL RECOLLECTIONS OF JULIUS WESS”, Int. J. Mod. Phys. Conf. Ser, 13:01 (2012), 158  crossref
    21. Cox B., Futorny V., Tirao J.A., “Djkm Algebras and Non-Classical Orthogonal Polynomials”, J. Differ. Equ., 255:9 (2013), 2846–2870  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    22. Cox B., Jurisich E., “Realizations of the Three-Point Lie Algebra Sl(2, R) Circle Plus (Omega(R)/Dr)”, Pac. J. Math., 270:1 (2014), 27–47  crossref  mathscinet  isi  scopus  scopus
    23. Cox B., Guo X., Lu R., Zhao K., “N-Point Virasoro Algebras and Their Modules of Densities”, Commun. Contemp. Math., 16:3 (2014), 1350047  crossref  mathscinet  zmath  isi  scopus  scopus
    24. O. K. Sheinman, “Lax operator algebras and integrable systems”, Russian Math. Surveys, 71:1 (2016), 109–156  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    25. Cox B., Jurisich E., Martins R.A., “The 3-point Virasoro algebra and its action on a Fock space”, J. Math. Phys., 57:3 (2016), 031702  crossref  mathscinet  zmath  isi  scopus
    26. Schlichenmaier M., “N -point Virasoro algebras are multipoint Krichever–Novikov-type algebras”, Commun. Algebr., 45:2 (2017), 776–821  crossref  mathscinet  zmath  isi  elib  scopus
    27. Cox B., Guo X., Lu R., Zhao K., “Simple Superelliptic Lie Algebras”, Commun. Contemp. Math., 19:3 (2017), 1650032  crossref  mathscinet  zmath  isi  scopus  scopus
    28. Cox B. Zhao K., “Certain Families of Polynomials Arising in the Study of Hyperelliptic Lie Algebras”, Ramanujan J., 46:2 (2018), 323–344  crossref  mathscinet  zmath  isi  scopus  scopus
    29. M. O. Katanaev, “Chern–Simons action and disclinations”, Proc. Steklov Inst. Math., 301 (2018), 114–133  mathnet  crossref  crossref  isi  elib  elib
    30. Cox B. Jurisich E. Martins R.A., “The Three Point Gauge Algebra Nu (Sic) Sl(2, R) Circle Plus (Omega(R)/Dr) and Its Action on a Fock Space”, J. Algebra, 521 (2019), 44–64  crossref  mathscinet  zmath  isi  scopus
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