Poisson structures on the center of the elliptic algebra A_{p,q}(sl(2)_c)

Abstract

It is shown that the elliptic algebra A_{p,q}(sl(2)_c) has a non trivial center at the critical level $c=-2$, generalizing the result of Reshetikhin and Semenov-Tian-Shansky for trigonometric algebras. A family of Poisson structures indexed by a non-negative integer $k$ is constructed on this center.

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References in corpus (2)

• Algebra of screening operators for the deformed $W_n$ algebra
• Elliptic algebra $A_{q,p}(\widehat{s{l}_2})$ in the scaling limit

Cited by in corpus (5)

• Classical and quantum q-deformed physical systems
• Central extensions of classical and quantum q-Viraroso algebras
• New ${\mathcal{W}}_{q,p}(sl(2))$ algebras from the elliptic algebra ${\mathcal{A}}_{q,p}(\hat{s}l(2{)}_c)$
• Deformed Virasoro algebras from elliptic quantum algebras
• q-deformed W-algebras and elliptic algebras