Classical Limit of the Scaled Elliptic Algebra $A_{\hbar,η}(sl_2)$

S. Khoroshkin; D. Lebedev; S. Pakuliak; A. Stolin; V. Tolstoy

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Classical Limit of the Scaled Elliptic Algebra $A_{\hbar,η}(sl_2)$

S. Khoroshkin·D. Lebedev·S. Pakuliak·A. Stolin·V. Tolstoy

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Abstract

The classical limit of the scaled elliptic algebra $A_{\hbar,η}(sl_2)$ 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 $A_{q,p}(sl_2)$ is also briefly presented.

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BibTeX RIS

S. Khoroshkin, D. Lebedev, S. Pakuliak, A. Stolin, V. Tolstoy. 1998-05-12. Classical Limit of the Scaled Elliptic Algebra $A_{\hbar,η}(sl_2)$. https://arxiv.org/abs/q-alg/9703043

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