Deformed \cal W_N Algebras from Elliptic sl ( N ) Algebras

1998/01/22 by Jean Avan, J. Avan, L. Frappat +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #hep-th #math.QA #msc:17B68 #msc:81R50 #nlin.SI #solv-int

paper · pdf · doi:10.1007/s002200050517

published as Commun.Math.Phys. 199 (1999) 697-728 · LaTeX2e Document - packages subeqn,amsfonts,amssymb - 30 pages

arxiv created 1998/01/22 · openalex publication_date 1999/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28

Abstract

We extend to the sl(N) case the results that we previously obtained on the construction of W_q,p algebras from the elliptic algebra A_q,p(sl(2)_c). The elliptic algebra A_q,p(sl(N)_c) at the critical level c=-N has an extended center containing trace-like operators t(z). Families of Poisson structures indexed by N(N-1)/2 integers, defining q-deformations of the W_N algebra, are constructed. The operators t(z) also close an exchange algebra when (-p¹/2)^NM = q^-c-N for M in Z. It becomes Abelian when in addition p=q^Nh where h is a non-zero integer. The Poisson structures obtained in these classical limits contain different q-deformed W_N algebras depending on the parity of h, characterizing the exchange structures at p ≠ q^Nh as new W_q,p(sl(N)) algebras.

Citations

• Quantum 401-1401-1401-1algebras and Macdonald polynomials
• A Coset-Type Construction for the Deformed Virasoro Algebra

Cited by

• Central extensions of classical and quantum q-Virasoro algebras