On spinor vertex operator algebras and their modules
type: Item
instance of: scholarly article
title: On spinor vertex operator algebras and their modules
zbMATH Open document ID: 0883.17027
published in: Journal of Algebra
publication date: 1997-08-26T00:00:00Z
review text: The author proves a generator theorem ensuring on a vector space \(V\) with a given set of fields \(S\) a structure of (colored) vertex operator algebra. The author also introduces an asymmetric tensor product of two colored vertex operator superalgebras with the same grading and supermap. These results are used for a characterization of a certain class of vertex operator superalgebras generated by fermionic fields. As a consequence the author gives a shorter proof of the Jacobi identity than the ones given in [\textit{A. J. Feingold}, \textit{I. B. Frenkel} and \textit{J. F. Ries}, Spinor construction of vertex operator algebras, triality and \(E_8^{(1)}\), Contemp. Math. 121 (1991; Zbl 0743.17029)] and [\textit{H. Tsukada}, Commun. Algebra 18, 2249-2274 (1990; Zbl 0704.17001)]. The author also gives a characterization of a certain class of twisted irreducible modules for spinor vertex operator algebras.
Mathematics Subject Classification ID: 17B69
Mathematics Subject Classification ID: 17A70
zbMATH DE Number: 1021745
zbMATH Keywords: generator theorem
zbMATH Keywords: vertex operator algebra
zbMATH Keywords: vertex operator superalgebras
zbMATH Keywords: Jacobi identity
zbMATH Keywords: twisted irreducible modules
author: Xiaoping Xu
reviewed by: Mirko Primc
MaRDI profile type: Publication
full work available at URL: jabr.1996.6971
OpenAlex ID: W2013404669
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DOI: 10.1006/JABR.1996.6971
description: scientific article; zbMATH DE number 1021745