Classical Limit of the Scaled Elliptic Algebra ${\mathcal A}$ħ,η ($\widehat{\mathfrak sl}$2)

Abstract

The classical limit of the scaled elliptic algebra${\mathcal A}$ħ,η ($\widehat{\mathfrak sl}$2) is investigated. The limiting Lie algebra is described in two equivalent ways: as a central extension of the algebra of generalized automorphic sl2 valued functions on a strip and as an extended algebra of decreasing automorphic sl2 valued functions on the real line. A bialgebra structure and an infinite-dimensional representation in the Fock space are studied. The classical limit of elliptic algebra ${\mathcal A}$q,p ($\widehat{\mathfrak sl}$2) is also briefly presented.