Classical Limit of the Scaled Elliptic Algebra A ℏ,η (s l 2 )
S. Khoroshkin, D. Lebedev, S. Pakuliak, A. Stolin, V. Tolstoy
Abstract
The classical limit of the scaled elliptic algebra
A
ℏ,η
(s
l
2
)
is investigated. The limiting Lie algebra is described in two equivalent ways: as a central extension of the algebra of generalized automorphic
s
l
2
valued functions on a strip and as an extended algebra of decreasing automorphic
s
l
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
(s
l
2
)
is also briefly presented.