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Regular version of the site

Article

Anti-Frobenius algebras and associative Yang-Baxter equation

Mathematical Models and Computer Simulations. 2014. Vol. 26. No. 11. P. 51-56.

Abstract. Associative Yang-Baxter equation arises in different areas of algebra, e.g.,
when studying double quadratic Poisson brackets, non-abelian quadratic Poisson brack-
ets, or associative algebras with cyclic 2-cocycle (anti-Frobenius algebras). Precisely,
faithful representations of anti-Frobenius algebras (up to isomorphism) are in one-to-one
correspondence with skew-symmetric solutions of associative Yang-Baxter equation (up
to equivalence). Following the work of Odesskii, Rubtsov and Sokolov and using comput-
er algebra system Sage, we found some constant skew-symmetric solutions of associative
Yang-Baxter equation and construct corresponded non-abelian quadratic Poisson brack-
ets.