| Abstract: | We present Feigin's construction Lectures given in Landau Institute] of latticeW algebras and give some simple results: lattice Virasoro andW
3 algebras. For the simplest caseg=sl(2), we introduce the wholeU
q(2)) quantum group on this lattice. We find the simplest two-dimensional module as well as the exchange relations and define the lattice Virasoro algebra as the algebra of invariants ofU
q(sl(2)). Another generalization is connected with the lattice integrals of motion as the invariants of the quantum affine groupU
q(ñ+). We show that Volkov's scheme leads to a system of difference equations for a function of non-commutative variables.Landau Institute for Theoretical Physics, 142432, Chernogolovka, Russia. Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No. 1, pp. 132–147, July, 1994. |
