Odd supersymmetrization of elliptic R-matrices *To the 80th anniversary of Andrei Slavnov. (10th April 2020)

• Record Type: Journal Article
• Authors: Levin, A; Olshanetsky, M; Zotov, A
• Is Part Of: Journal of physics. Volume 53:Number 18(2020)
• Publication Date: 2020-04-10
• Subjects: elliptic R-matrix -- Yang–Baxter equations -- supersymmetric elliptic curve; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab7e53
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We study a general ansatz for an odd supersymmetric version of the Kronecker elliptic function, which satisfies the genus one Fay identity. The obtained result is used for construction of the odd supersymmetric analogue for the classical and quantum elliptic R -matrices. They are shown to satisfy the classical Yang–Baxter equation and the associative Yang–Baxter equation. The quantum Yang–Baxter equation is discussed as well. It acquires additional term in the case of supersymmetric R -matrices.