Modules over the Heisenberg-Virasoro and $W(2,2)$ algebras

Abstract

In this paper, we consider the modules for the Heisenberg-Virasoro algebra and the W algebra $W(2,2)$. We determine the modules whose restriction to the Cartan subalgebra (modulo center) are free of rank $1$ for the two algebras. We also determine the simplicity of these modules. These modules provide new simple modules for the W algebra $W(2,2)$.

References in corpus (4)

• Simple sl_{n+1}-module structures on U(h)
• $\mathcal{U}(\mathfrak{h})$-free modules and coherent families
• Irreducible modules over Witt algebras ${\mathcal{W}}_n$ and over ${\mathfrak{sl}}_{n+1}(\mathbb{C})$
• $\W_n^+$- and $W_n$-module structures on $U(h)$

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• Module structure on $U(\mathfrak{h})$ for Kac-Moody algebras
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• Regularity of quasigeodesics characterises hyperbolicity
• Measures and generalizations of dual Littlewood identities
• Simple non-weight modules over Lie superalgebras of Block type
• Simple $\mathfrak{sl}(V)$-modules which are free over an abelian subalgebra
• Irreducible twisted Heisenberg-Virasoro modules from tensor products
• Modules over the algebra $\mathcal{V}ir(a,b)$
• Loop W(a,b) Lie conformal algebra