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Classification of irreducible quasifinite modules over map Virasoro algebras

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Abstract

We give a complete classification of the irreducible quasifinite modules for algebras of the form Vir ⊗ A, where Vir is the Virasoro algebra and A is a finitely generated commutative associative unital algebra over the complex numbers. It is shown that all such modules are tensor products of generalized evaluation modules. We also give an explicit sufficient condition for a Verma module of Vir ⊗ A to be reducible. In the case that A is an infinite-dimensional integral domain, this condition is also necessary.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada

    Alistair Savage

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  1. Alistair Savage
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Correspondence to Alistair Savage.

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This work was supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada.

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Savage, A. Classification of irreducible quasifinite modules over map Virasoro algebras. Transformation Groups 17, 547–570 (2012). https://doi.org/10.1007/s00031-012-9182-9

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  • DOI: https://doi.org/10.1007/s00031-012-9182-9

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