Classification of irreducible weight modules over higher rank Virasoro algebras

By R. Lu, Kaiming Zhao. 2003

69 citations recorded by the source corpus.

Let G be a rank n additive subgroup of C and Vir[G] the corresponding Virasoro algebra of rank n. In the present paper, irreducible weight modules with finite dimensional weight spaces over Vir[G] are completely determined. There are two different classes of them. One class consists of simple modules of intermediate series whose weight spaces are all 1-dimensional. The other is constructed by using intermediate series modules over a Virasoro subalgebra of rank n−1. The classification of such modules over the classical Virasoro algebra was obtained by O. Mathieu in 1992 using a completely different approach.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/882b417f0b3b7eaee0dd2019d9db586d4454d8ca

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In Algebra and Number Theory

1. Xiangqian Guo
2. R. Lu
3. Kaiming Zhao

In Geometry and Topology

1. Xiangqian Guo
2. R. Lu
3. Kaiming Zhao

In Mathematical Physics

1. Xiangqian Guo
2. Kaiming Zhao
3. R. Lu

Citations in the corpus

• Simple Harish-Chandra modules, intermediate series modules, and Verma modules over the loop-Virasoro algebra (2010, methodology): “From our proofs in Sections 3 and 4, one can easily see that the method we have employed here is conceptional and non-computational, which is totally different from those used in [23], [19] and [20].”