Automorphism groups of parafermion vertex operator algebras: general case

2024/04/26 by Lam, Ching Hung, Lin, Xingjun, Shimakura, Hiroki
#20B25 #FOS: Mathematics #Group Theory (math.GR) #Primary 17B69 #Quantum Algebra (math.QA) #Secondary 17B22

paper · doi:10.48550/arxiv.2404.17096

Abstract

We complete the program for determining the full automorphism groups of all parafermion vertex operator algebras associated with simple Lie algebras and positive integral levels. We show that the full automorphism group of the parafermion vertex operator algebra is isomorphic to the automorphism group of the associated root system for the remaining cases: (i) the level is at least 3; (ii) the level is 2 and the simple Lie algebra is non simply laced.

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• Parafermion vertex operator algebras and W-algebras
• Generalized vertex algebras generated by parafermion-like vertex operators
• The structure of parafermion vertex operator algebras: general case
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