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

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

1997-03-27

arxiv.org/abs/q-alg/9703043v2

Mathematics

Quantum Algebra

LaTeX 2.09, 2 figs under bezier.sty, macros use AMS fonts, 18 pages One incorrect statement is corrected, note and 3 ref. are

Scientific paper

The classical limit of the scaled elliptic algebra $A_{\hbar,\eta}(sl_2)$ 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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