Deformed W_N algebras from elliptic sl(N) algebras
摘要
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}(\hat{sl}(2)_c). The elliptic algebra A_{q,p}(\hat{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 (-p^1/2)^{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 \ne q^{Nh} as new W_{q,p}(sl(N)) algebras.
引用
@article{arxiv.math/9801105,
title = {Deformed W_N algebras from elliptic sl(N) algebras},
author = {J. Avan and L. Frappat and M. Rossi and P. Sorba},
journal= {arXiv preprint arXiv:math/9801105},
year = {2009}
}
备注
LaTeX2e Document - packages subeqn,amsfonts,amssymb - 30 pages