On ABCD algebras and associative Yang-Baxter equations

In the present paper we consider the usage of associative Yang-Baxter equations in the theory of classical and quantum ABCD algebras [1]. Classical and quantum associative analogs of the generalized Fredel-Maillet equations for ABCD tensors [2, 3] are found. Two classes of examples — rational and trigonometric — of classical and quantum ABCD tensors satisfying these equations are considered in details.