Yang–Baxter equations with two Planck constants. (7th December 2015) - Levin, A; Olshanetsky, M; Zotov, A
Abstract: 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 Sklyanin elliptic algebras. Then we proceed to a natural generalization of the Baxter–Belavin quantum R -matrix to the case It can be viewed as symmetric form of 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.