Realization of ω ∞-algebras and Uq( sl(2)) in terms of generalized Clifford algebras

Abstract

We consider the generalized Clifford algebras (GCA) and an infinite set of their subalgebras. We obtain the realization of some infinite-dimensional Lie algebras. More precisely, we show that the quantum tori Lie algebra and Witt algebra, its high spin extension ω ∞-algebra, and quantum enveloping algebra U q ( sl(2)) can be realized in terms of generators of generalized Clifford algebras. We also discuss the connection between gl( N, C ) and GCA.