Heisenberg VOAs over fields of prime characteristic and their representations

Li, Haisheng; Mu, Qiang

doi:10.1090/tran/7094

Heisenberg VOAs over fields of prime characteristic and their representations
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by Haisheng Li and Qiang Mu PDF

Trans. Amer. Math. Soc. 370 (2018), 1159-1184 Request permission

Abstract:

In this paper, we study Heisenberg vertex algebras over fields of prime characteristic. The new feature is that the Heisenberg vertex algebras are no longer simple unlike in the case of characteristic zero. We then study a family of simple quotient vertex algebras and we show that for each such simple quotient vertex algebra, irreducible modules are unique up to isomorphism and every module is completely reducible. This gives us a family of rational modular vertex algebras in a certain sense. To achieve our goal, we also establish a complete reducibility theorem for a certain category of modules over Heisenberg algebras.

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