Yang–Baxter equations with two Planck constants. (7th December 2015)

• Record Type: Journal Article
• Authors: Levin, A; Olshanetsky, M; Zotov, A
• Is Part Of: Journal of physics. Volume 49:Number 1(2016)
• Publication Date: 2015-12-07
• Subjects: quantum R-matrices -- Yang–Baxter equation -- integrable systems; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/49/1/014003
• Languages: English
• ISSNs: 1751-8113

Abstract

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.