Abstract
Let Cq be the non-commutative Laurent polynomial ring associated with a (n+1)×(n+1) rational quantum matrix q. Let sld(Cq)⊕HC1(Cq) be the universal central extension of Lie subalgebra sld(Cq) of gld(Cq). We take the Lie algebra τ=gld(Cq)⊕HC1(Cq). Let Der(Cq) be the Lie algebra of all derivations of Cq and consider the Lie algebra τ˜=τ⋊Der(Cq), called the full toroidal Lie algebra coordinated by rational quantum tori. In this paper we get a classification of irreducible integrable modules with finite dimensional weight spaces for τ˜ with nonzero central action on the modules.
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