Central extensions of classical and quantum q-Virasoro algebras

1998/06/11 by Jean Avan, J. Avan, L. Frappat +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.QA #msc:17B37 #msc:81R50

paper · pdf · doi:10.1016/s0375-9601(98)00864-0

published as Phys.Lett. A251 (1999) 13 · Latex2e, needs amsfonts and amssymb packages

arxiv created 1998/06/11 · openalex publication_date 1999/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the central extensions of the q-deformed (classical and quantum) Virasoro algebras constructed from the elliptic quantum algebra A_q,p[sl(N)_c]. After establishing the expressions of the cocycle conditions, we solve them, both in the classical and in the quantum case (for sl(2)). We find that the consistent central extensions are much more general that those found previously in the literature.

Citations

• Massless XXZ Model and Degeneration of the Elliptic Algebra A_q,p(\widehatsl₂)
• Quantum 401-1401-1401-1algebras and Macdonald polynomials
• Quantum affine algebras and deformations of the Virasoro and 237-1237-1237-1
• Virasoro-type Symmetries in Solvable Models
• A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions
• Deformed \cal W_N Algebras from Elliptic sl ( N ) Algebras