Anti-Frobenius algebras and associative Yang–Baxter equation
A. I. Zobnin
Lomonosov Moscow State University, Department of Mechanics and Mathematics, Moscow
Associative Yang–Baxter equation arises in different areas of algebra, e.g., when studying double quadratic Poisson brackets, non-abelian quadratic Poisson brackets, 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 computer algebra system Sage, we found some constant skew-symmetric solutions of associative Yang–Baxter equation and construct corresponded non-abelian quadratic Poisson brackets.
associative Yang–Baxter equation, anti-Frobenius algebras, non-abelian quadratic Poisson brackets.
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A. I. Zobnin, “Anti-Frobenius algebras and associative Yang–Baxter equation”, Matem. Mod., 26:11 (2014), 51–56
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\paper Anti-Frobenius algebras and associative Yang--Baxter equation
\jour Matem. Mod.
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