Yang-Baxter equations with two Planck constants

We consider Yang-Baxter equations arising from its associative analog and study the corresponding exchange relations. They generate finite-dimensional quantum algebras which have the form of coupled GL(N) Sklyanin elliptic algebras. Then we proceed to a natural generalization of the Baxter-Belavin quantum R-matrix to the case Mat(N, C)(circle times 2) circle times Mat(M, C)(circle times 2). It can be viewed as symmetric form of GL(NM) R-matrix in the sense that the Planck constant and the spectral parameter enter (almost) symmetrically. Such type (symmetric) R-matrices are also shown to satisfy the Yang-Baxter like quadratic and cubic equations.