Theoretical and Mathematical Physics

, Volume 100, Issue 1, pp 900–911 | Cite as

LatticeW algebras and quantum groups

  • Ya. P. Pugay


We present Feigin's construction [Lectures given in Landau Institute] of latticeW algebras and give some simple results: lattice Virasoro andW3 algebras. For the simplest caseg=sl(2), we introduce the wholeUq(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 ofUq(sl(2)). Another generalization is connected with the lattice integrals of motion as the invariants of the quantum affine groupUq+). We show that Volkov's scheme leads to a system of difference equations for a function of non-commutative variables.


Difference Equation Quantum Group Exchange Relation Simple Result Lattice Integral 
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© Plenum Publishing Corporation 1995

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  • Ya. P. Pugay

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