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Singular vectors and Zhu’s Poisson algebra of parafermion vertex operator algebras. (English) Zbl 1269.81062

Dobrev, Vladimir (ed.), Lie theory and its applications in physics. IX international workshop. Based on the 9th workshop on Lie theory and its applications in physics, Varna, Bulgaria, June 20–26, 2011. Tokyo: Springer (ISBN 978-4-431-54269-8/hbk; 978-4-431-54270-4/ebook). Springer Proceedings in Mathematics & Statistics 36, 391-398 (2013).
Summary: We study Zhu’s Poisson algebra of parafermion vertex operator algebras associated with integrable highest weight modules for the affine Kac-Moody Lie algebra \(\widehat{sl}_{2}\). Using singular vectors, we show that the parafermion vertex operator algebras are \(C_2\)-cofinite and rational.
For the entire collection see [Zbl 1266.00027].

MSC:

17B63 Poisson algebras
17B69 Vertex operators; vertex operator algebras and related structures
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References:

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