Classical limit of the scaled elliptic algebra A(h,eta)((sl)over-cap(2))

Journal article, 1999

The classical limit of the scaled elliptic algebra A((h) over bar eta)(<(sl)over cap>(2)) is investigated. The limiting Lie algebra is described in two equivalent ways: as a central extension of the algebra of generalized automorphic sl(2) valued functions on a strip and as an extended algebra of decreasing automorphic sl(2) 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 A(q,p)(<(sl)over cap>(2)) is also briefly presented.