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Noetherianity of twisted Zhu’s algebras and bimodules

Part of: Lie algebras and Lie superalgebras Modules, bimodules and ideals Chain conditions, growth conditions, and other forms of finiteness

Published online by Cambridge University Press:  03 February 2025

Jianqi Liu Open the ORCID record for Jianqi Liu [Opens in a new window]
Jianqi Liu*
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, PA, USA
*
Email: jliu230@sas.upenn.edu
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Abstract

In this paper, we show that for a large natural class of vertex operator algebras (VOAs) and their modules, the Zhu’s 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.

Keywords

vertex operator algebraassociative algebratwisted representationfusion rulesNoether ring

MSC classification

Primary: 17B69: Vertex operators; vertex operator algebras and related structures
Secondary: 16D10: General module theory 17B10: Representations, algebraic theory (weights) 16P40: Noetherian rings and modules
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , First View , pp. 1 - 30
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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