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arXiv · 1903.06882

Classification of irreducible Harish-Chandra modules over gap-$p$ Virasoro algebras

Chengkang Xu
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Abstract

We prove that any irreducible Harish-Chandra modules for a class of Lie algebras, which we call gap-$p$ Virasoro algebras, must be a highest weight module, a lowest weight module, or a module of intermediate series.These algebras are closely related to the Heisenberg-Virasoro algebra and the algebra of derivations over a quantum torus. They also contain subalgebras which are isomorphic to the Virasoro algebra $Vir$, but graded by $p\mathbb Z$(unlike $Vir$ by $\mathbb Z$).

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BibTeXRIS

Chengkang Xu. 2019-10-31. Classification of irreducible Harish-Chandra modules over gap-$p$ Virasoro algebras. https://doi.org/10.1016/j.jalgebra.2019.09.023

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