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
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.
Received: November 2, 2001; in revised form April 8, 2002
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
\paper Set-theoretical solutions to the Yang--Baxter relation from factorization of matrix polynomials and $\theta$-functions
\jour Mosc. Math.~J.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
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
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
Odesskii A.V., Sokolov V.V., “Compatible Lie brackets related to elliptic curve”, J. Math. Phys., 47:1 (2006), 013506, 14 pp.
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
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
|Number of views:|