Noetherianity of twisted Zhu algebra and bimodules

2021/03/15 by Liu, Jianqi
#13A02 #16D20 #16P40 #17B69 #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2103.08090

Abstract

In this paper we show that for a large natural class of vertex operator algebras (VOAs) and their modules, the Zhu algebras and bimodules (and their g-twisted analogs) are Noetherian. These carry important information about the representation theory of the VOA, and its fusion rules, and the Noetherian property gives the potential for (non-commutative) algebro-geometric methods to be employed in their study.

Related

• Twisted regular representations and bimodules in vertex operator algebra theory
• Bimodules over twisted Zhu algebras and twisted fusion rules theorem for vertex operator algebras
• Zhu's algebra, the C₂ algebra, and twisted modules
• Bimodules and g-rationality of vertex operator algebras
• Twisted bimodules and associative algebras associated to VOAs