Non-weight modules over algebras related to the Virasoro algebra

Abstract

In this paper, we study a class of non-weight modules over two kinds of algebras related to the Virasoro algebra, i.e., the loop-Virasoro algebras $\mathfrak{L}$ and a class of Block type Lie algebras $\mathfrak{B}(\mathfrak{q})$, where $q$ is a nonzero complex number. We determine those modules whose restriction to the Cartan subalgebra (modulo center) are free of rank one. We also provide a sufficient and necessary condition for such modules to be simple, and determine their isomorphism classes. Moreover, we obtain the simplicity of modules over loop-Virasoro algebras by taking tensor products of some irreducible modules mentioned above with irreducible highest weight modules or Whittaker modules.

arXiv comment14 pages. Comments are welcome

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Cited by in corpus (7)

• A family of non-weight modules over the super-Virasoro algebras
• Non-weight modules over the affine-Virasoro algebra of type $A_1$
• A family of simple non-weight modules over the twisted $N=2$ superconformal algebra
• On non-weight representations of the $N=2$ superconformal algebras
• Measures and generalizations of dual Littlewood identities
• On a family of non-weight modules over Virasoro-type Lie (super)algebras
• Simple non-weight modules over Lie superalgebras of Block type