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Heisenberg VOAs over fields of prime characteristic and their representations


Authors: Haisheng Li and Qiang Mu
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 17B69
DOI: https://doi.org/10.1090/tran/7094
Published electronically: July 7, 2017
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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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Haisheng Li
Affiliation: Department of Mathematical Sciences, Rutgers University, Camden, New Jersey 08102 – and – School of Mathematical Sciences, Xiamen University, Xiamen 361005, People’s Republic of China
Email: hli@camden.rutgers.edu

Qiang Mu
Affiliation: School of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang 150025, People’s Republic of China
Email: qmu520@gmail.com

DOI: https://doi.org/10.1090/tran/7094
Received by editor(s): May 31, 2016
Published electronically: July 7, 2017
Additional Notes: The first-named author was partially supported by China NSF grant No. 11471268. The second-named author was supported by NSFC grant No. 11571391, Heilongjiang Provincial Natural Science Foundation grant No. LC2015001, and Program for NCET in Heilongjiang Provincial University grant No. 1254--NCET--010. The second-named author is the corresponding author
Article copyright: © Copyright 2017 American Mathematical Society