  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.
