Irreducible integrable modules for the full toroidal Lie algebras coordinated by rational quantum torus

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