30 research outputs found
Set-theoretical solutions to the Yang-Baxter Relation from factorization of matrix polynomials and -functions
New set-theoretical solutions to the Yang-Baxter Relation are constructed.
These solutions arise from the decompositions "in different order" of matrix
polynomials and -functions. We also construct a "local action of the
symmetric group" in these cases, generalizations of the action of the symmetric
group given by the set-theoretical solution.Comment: 9 pages, to appear in Moscow Math Journa
Compatible quadratic Poisson brackets related to a family of elliptic curves
We construct nine pairwise compatible quadratic Poisson structures such that
a generic linear combination of them is associated with an elliptic algebra in
n generators. Explicit formulas for Casimir elements of this elliptic Poisson
structure are obtained.Comment: 17 pages, Latex, major change