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Working paper

Yang-Baxter equations with two Planck constants

Levin A., Olshanetsky M., Zotov A.
We consider Yang-Baxter equations arising from its associative analog and study corresponding exchange relations. They generate finite-dimensional quantum algebras which have 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) ⊗ Mat(N, C) ⊗Mat(M, C) ⊗ Mat(M, C) . 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.