Bounded weight modules of the Lie algebra of vector fields on \mathbb C²

2016/11/06 by Andrew Cavaness, Cavaness, Andrew, Dimitar Grantcharov +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1611.01821

Abstract

We study weight modules of the Lie algebra W₂ of vector fields on \mathbb C². A classification of all simple weight modules of W₂ with a uniformly bounded set of weight multiplicities is provided. To achieve this classification we introduce a new family of generalized tensor W_n-modules. Our classification result is an important step in the classification of all simple weight W_n-modules with finite weight multiplicities.

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• Classification of simple bounded weight modules of the Lie algebra of vector fields on \Cⁿ
• Simple weight modules with finite weight multiplicities over the Lie algebra of polynomial vector fields
• bounded weight modules over the Lie superalgebra of Cartan W-type
• Weight modules for current algebras
• Simple weight modules with finite-dimensional weight spaces over Witt superalgebras