Lattice W algebras and quantum groups
Abstract
We present Feigin's construction [Lectures given in Landau Institute] of lattice W algebras and give some simple results: lattice Virasoro and W _{3} algebras. For the simplest case g=sl(2), we introduce the whole U _{q}(2)) quantum group on this lattice. We find the simplest twodimensional module as well as the exchange relations and define the lattice Virasoro algebra as the algebra of invariants of U _{q}( sl(2)). Another generalization is connected with the lattice integrals of motion as the invariants of the quantum affine group U _{q}(ñ_{+}). We show that Volkov's scheme leads to a system of difference equations for a function of noncommutative variables.
 Publication:

Theoretical and Mathematical Physics
 Pub Date:
 July 1994
 DOI:
 10.1007/BF01017329
 arXiv:
 arXiv:hepth/9307127
 Bibcode:
 1994TMP...100..900P
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 13 pages, misprints have been corrected