q-deformed W-algebras and elliptic algebras - Université Pierre et Marie Curie Accéder directement au contenu
Article Dans Une Revue Czechoslovak Journal of Physics Année : 1998

q-deformed W-algebras and elliptic algebras

Résumé

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, 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 $p =/ q^{Nh}$ as new $W_{q,p}(sl(N))$ algebras.

Dates et versions

hal-00376656 , version 1 (19-04-2009)

Identifiants

Citer

Jean Avan, L. Frappat, M. Rossi, P. Sorba. q-deformed W-algebras and elliptic algebras. Czechoslovak Journal of Physics, 1998, 48, pp.1291. ⟨hal-00376656⟩
170 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More