Classical Limit of the Scaled Elliptic Algebra ${\mathcal A}$ħ,η ($\widehat{\mathfrak sl}$2)
KHOROSHKIN, S.; LEBEDE, D.; PAKULIAK, S.; STOLIN, A.; TOLSTOY, V.; KHOROSHKIN S.; Institute of Theoretical and Experimental Physics; LEBEDE D.; Institute of Theoretical and Experimental Physics; PAKULIAK S.; JINR; Bogoliubov Institute of Theoretical Physics; STOLIN A.; Göteborg University; TOLSTOY V.; Moscow State University
Журнал:
Compositio Mathematica
Дата:
1999
Аннотация:
The classical limit of the scaled elliptic algebra${\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.
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