Classification of irreducible weight modules with a finite dimensional weight space over twisted Heisenberg-Virasoro algebra

2005/12/10 by Ran Shen, Shen, Ran, Yucai Su +1 · 1 citation
Mathematics · #17B56 #17B68 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0512209

openalex publication_date 2005/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenberg-Virasoro algebra, having a nontrivial finite dimensional weight space, is a Harish-Chandra module (and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series

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• Simple restricted modules of non-zero level over a deformed Heisenberg-Virasoro algebra

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