# zbMATH — the first resource for mathematics

The quantum bialgebra associated with the eight-vertex $$R$$-matrix. (English) Zbl 0774.17024
Summary: The quantum bialgebra related to the Baxter’s eight-vertex $$R$$-matrix is found as a quantum deformation of the Lie algebra of $$\text{sl}(2)$$- valued automorphic functions on a complex torus.

##### MSC:
 17B37 Quantum groups (quantized enveloping algebras) and related deformations 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
Full Text:
##### References:
 [1] Baxter, R. J.,Ann. Phys. 76, 1 (1973). · Zbl 1092.82511 · doi:10.1016/0003-4916(73)90439-9 [2] Reyman, A. G. and Semenov-Tyan-Shanskii, M. A.,J. Soviet Math. 46, 1631 (1989). · Zbl 0673.35093 · doi:10.1007/BF01099195 [3] Belavin, A. A. and Drinfel’d V. G.,Funct. Anal. Appl. 17, 220 (1984). · Zbl 0533.22014 · doi:10.1007/BF01078107 [4] Sklyanin, E. K.,Funct. Anal. Appl. 16, 263 (1983). · Zbl 0513.58028 · doi:10.1007/BF01077848 [5] Drinfel’d V. G.,Proc. ICM, Berkeley, CA, U.S.A., 798 (1986). [6] Chari, V. and Pressley, A.,Enseign. Math. (2)36, 267 (1990);Comm. Math. Phys. 142, 261 (1991). [7] Uglov, D. B., to be published.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.