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Mosc. Math. J., 2003, Volume 3, Number 1, Pages 97–103 (Mi mmj78)  

This article is cited in 8 scientific papers (total in 8 papers)

Set-theoretical solutions to the Yang–Baxter relation from factorization of matrix polynomials and $\theta$-functions

A. V. Odesskii

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: New set-theoretical solutions to the Yang–Baxter Relation are constructed. These solutions arise from the decompositions “in different order” of matrix polynomials and $\theta$-functions. We also construct a “local action of the symmetric group” in these cases, generalizations of the action of the symmetric group $S_N$ given by the set-theoretical solution.

Key words and phrases: Yang–Baxter relation, set-theoretical solution, local action of the symmetric group, matrix polynomials, matrix $\theta$-functions.

DOI: https://doi.org/10.17323/1609-4514-2003-3-1-97-103

Full text: http://www.ams.org/.../abst3-1-2003.html
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MSC: 81R50
Received: November 2, 2001; in revised form April 8, 2002
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Citation: A. V. Odesskii, “Set-theoretical solutions to the Yang–Baxter relation from factorization of matrix polynomials and $\theta$-functions”, Mosc. Math. J., 3:1 (2003), 97–103

Citation in format AMSBIB
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\by A.~V.~Odesskii
\paper Set-theoretical solutions to the Yang--Baxter relation from factorization of matrix polynomials and $\theta$-functions
\jour Mosc. Math.~J.
\yr 2003
\vol 3
\issue 1
\pages 97--103
\mathnet{http://mi.mathnet.ru/mmj78}
\crossref{https://doi.org/10.17323/1609-4514-2003-3-1-97-103}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1996805}
\zmath{https://zbmath.org/?q=an:1052.81050}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208594100008}


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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. Borodin A., “Isomonodromy transformations of linear systems of difference equations”, Ann. of Math. (2), 160:3 (2004), 1141–1182  crossref  mathscinet  isi
    2. Adler V.E., Bobenko A.I., Suris Yu.B., “Geometry of Yang–Baxter maps: pencils of conics and quadrirational mappings”, Comm. Anal. Geom., 12:5 (2004), 967–1007  crossref  mathscinet  zmath  isi
    3. Gelfand I., Retakh V., Serconek S., Wilson R., “On a class of algebras associated to directed graphs”, Selecta Math. (N.S.), 11:2 (2005), 281–295  crossref  mathscinet  zmath  isi
    4. Odesskii A.V., Sokolov V.V., “Compatible Lie brackets related to elliptic curve”, J. Math. Phys., 47:1 (2006), 013506, 14 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Maldonado C., Mombelli J.M., “On braided groupoids”, J. Algebra, 307:2 (2007), 677–694  crossref  mathscinet  zmath  isi
    6. Retakh V., Serconek Sh., Wilson R.L., “Construction of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials”, Lie Algebras, Vertex Operator Algebras and their Applications, Contemporary Mathematics Series, 442, 2007, 201–219  crossref  mathscinet  zmath  isi
    7. Tsuboi Z., “Quantum Groups, Yang-Baxter Maps and Quasi-Determinants”, Nucl. Phys. B, 926 (2018), 200–238  crossref  mathscinet  zmath  isi  scopus
    8. Bazhanov V.V., Sergeev S.M., “Yang-Baxter Maps, Discrete Integrable Equations and Quantum Groups”, Nucl. Phys. B, 926 (2018), 509–543  crossref  mathscinet  zmath  isi  scopus
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