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

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Moscow Mathematical Journal, 2003, Volume 3, Number 1, Pages 97–103
DOI: https://doi.org/10.17323/1609-4514-2003-3-1-97-103 (Mi mmj78)

This article is cited in 10 scientific papers (total in 10 papers)

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

θ

$\theta$ -functions

A. V. Odesskii

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

Full-text PDF Citations (10)

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

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

θ

$\theta$ -functions. We also construct a “local action of the symmetric group” in these cases, generalizations of the action of the symmetric group

S_{N}

$S_N$ 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

θ

$\theta$ -functions.

Received: November 2, 2001; in revised form April 8, 2002

Bibliographic databases:

MSC: 81R50

Language: English

Citation: A. V. Odesskii, “Set-theoretical solutions to the Yang–Baxter relation from factorization of matrix polynomials and

θ

$\theta$ -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://mathscinet.ams.org/mathscinet-getitem?mr=1996805}

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Linking options:

https://www.mathnet.ru/eng/mmj78

https://www.mathnet.ru/eng/mmj/v3/i1/p97

This publication is cited in the following 10 articles:

Andrew P. Kels, “Two-component Yang–Baxter maps and star-triangle relations”, Physica D: Nonlinear Phenomena, 448 (2023), 133723
Retakh V., Saks M., “On the Rational Relationships Among Pseudo-Roots of Anon-Commutative Polynomial”, J. Pure Appl. Algebr., 225:6 (2021), 106581
Tsuboi Z., “Quantum Groups, Yang-Baxter Maps and Quasi-Determinants”, Nucl. Phys. B, 926 (2018), 200–238
Bazhanov V.V., Sergeev S.M., “Yang-Baxter Maps, Discrete Integrable Equations and Quantum Groups”, Nucl. Phys. B, 926 (2018), 509–543
Maldonado C., Mombelli J.M., “On braided groupoids”, J. Algebra, 307:2 (2007), 677–694
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
Odesskii A.V., Sokolov V.V., “Compatible Lie brackets related to elliptic curve”, J. Math. Phys., 47:1 (2006), 013506, 14 pp.
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
Borodin A., “Isomonodromy transformations of linear systems of difference equations”, Ann. of Math. (2), 160:3 (2004), 1141–1182
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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