Classification of irreducible quasifinite modules over map Virasoro algebras

Details Classification of irreducible quasifinite modules over map Virasoro algebras Classification of irreducible quasifinite modules over map Virasoro algebras

2011-07-21

arxiv.org/abs/1107.4365v2

Mathematics

Representation Theory

25 pages. v2: Minor changes, published version

Scientific paper

We give a complete classification of the irreducible quasifinite modules for algebras of the form Vir \otimes A, where Vir is the Virasoro algebra and A is a Noetherian 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 \otimes A to be reducible. In the case that A is an infinite-dimensional integral domain, this condition is also necessary.

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