Supports of weight modules over Witt algebras

2009/06/04 by Volodymyr Mazorchuk, Kaiming Zhao, Mazorchuk, Volodymyr +1 · 2 citations
Mathematics · #17B10 #17B20 #17B65 #17B66 #17B68 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0906.0947

openalex publication_date 2009/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, as the first step towards classification of simple weight modules with finite dimensional weight spaces over Witt algebras W_n, we explicitly describe supports of such modules. We also obtain some descriptions on the support of an arbitrary simple weight module over a \Zⁿ-graded Lie algebra \mathfrakg having a root space decomposition ⊕_α∈\Zⁿ\mathfrak g_α with respect to the abelian subalgebra \mathfrak g₀, with the property [\mathfrakg_α,\mathfrak g_β]= \mathfrak g_α+β for all α,β∈\Zⁿ, α≠ β (this class contains the algebra W_n).

Cited by

• Classification of irreducible Harish-Chandra modules over map full toroidal Lie algebras
• Quasi-derivations of Witt and related algebras

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