On certain vertex algebras and their modules associated with vertex algebroids

Details On certain vertex algebras and their modules associated with vertex algebroids On certain vertex algebras and their modules associated with vertex algebroids

2004-10-20

arxiv.org/abs/math/0410446v1

Mathematics

Quantum Algebra

32 pages. Journal of Algebra, in Press

Scientific paper

We study the family of vertex algebras associated with vertex algebroids, constructed by Gorbounov, Malikov, and Schechtman. As the main result, we classify all the (graded) simple modules for such vertex algebras and we show that the equivalence classes of graded simple modules one-to-one correspond to the equivalence classes of simple modules for the Lie algebroids associated with the vertex algebroids. To achieve our goal, we construct and exploit a Lie algebra from a given vertex algebroid.

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