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Matem. Mod., 2014, Volume 26, Number 11, Pages 51–56 (Mi mm3539)  

Anti-Frobenius algebras and associative Yang–Baxter equation

A. I. Zobnin

Lomonosov Moscow State University, Department of Mechanics and Mathematics, Moscow

Abstract: 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.

Keywords: associative Yang–Baxter equation, anti-Frobenius algebras, non-abelian quadratic Poisson brackets.

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Bibliographic databases:
UDC: 512.552
Received: 21.03.2014
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Citation: A. I. Zobnin, “Anti-Frobenius algebras and associative Yang–Baxter equation”, Matem. Mod., 26:11 (2014), 51–56

Citation in format AMSBIB
\Bibitem{Zob14}
\by A.~I.~Zobnin
\paper Anti-Frobenius algebras and associative Yang--Baxter equation
\jour Matem. Mod.
\yr 2014
\vol 26
\issue 11
\pages 51--56
\mathnet{http://mi.mathnet.ru/mm3539}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3541375}
\elib{https://elibrary.ru/item.asp?id=23421439}


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