Non-weight representations of Lie superalgebras of Block type, I

Abstract

In this paper, we study non-weight representations of two classes of Lie algebras and two classes of Lie superalgebras of Block type. More precisely, we completely classify the free U(h)-modules of rank one or two over these Lie superalgebras. Then we determine the simplicity and isomorphism classes of these modules. As a byproduct, we also obtain the non-weight representation results for a class of non-semisimple finitely graded extensions of the Virasoro algebra.