Geodesic
Anti-Frobenius algebras and associative Yang--Baxter equation
Matematičeskoe modelirovanie, Tome 26 (2014) no. 11, pp. 51-56

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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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     author = {A. I. Zobnin},
     title = {Anti-Frobenius algebras and associative {Yang--Baxter} equation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {51--56},
     publisher = {mathdoc},
     volume = {26},
     number = {11},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MM_2014_26_11_a7/}
}
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A. I. Zobnin. Anti-Frobenius algebras and associative Yang--Baxter equation. Matematičeskoe modelirovanie, Tome 26 (2014) no. 11, pp. 51-56. http://geodesic.mathdoc.fr/item/MM_2014_26_11_a7/