Exotic Particles and $w_\infty$-Algebras in Two- and High-Dimensional Spaces

Abstract

We construct a set of noncommuting translation operators in two and high-dimensional lattices. The algebras they close are $w_{\infty}$-algebras. The construction is based on the introduction of noncommmuting elementary link operators which link two neighborhood sites in the lattice. This kind of operators preserve the braiding nature of exotic particles living basically in two-dimensional space.