Set-theoretical solutions to the Yang-Baxter Relation from factorization of matrix polynomials and $θ$-functions

Details Set-theoretical solutions to the Yang-Baxter Relation from factorization of matrix polynomials and $θ$-functions Set-theoretical solutions to the Yang-Baxter Relation from factorization of matrix polynomials and $θ$-functions

2002-05-06

arxiv.org/abs/math/0205051v1

Mathematics

Quantum Algebra

9 pages, to appear in Moscow Math Journal

Scientific paper

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.

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