Non-weight modules over the affine-Virasoro algebra of type A1

Abstract

In this paper, we study a class of non-weight modules over the affine-Virasoro algebra of type A1, which are free modules of rank one when restricted to the Cartan subalgebra (modulo center). We give the classification of such modules. Moreover, the simplicity and the isomorphism classes of these modules are determined.

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