Binary codes and vertex operator (super)algebras
type: Item
instance of: scholarly article
title: Binary codes and vertex operator (super)algebras
zbMATH Open document ID: 0857.17026
author: Masahiko Miyamoto
published in: Journal of Algebra
publication date: 1996-07-09T00:00:00Z
review text: The author studies vertex operator algebras whose Virasoro element is a sum of pairwise orthogonal rational conformal vectors with central charge \({1\over2}\), the most important example being the moonshine module \(V^\natural\). In the paper under review the author constructs a simple vertex operator algebra \(M_D\) for an even binary code \(D\subset \mathbb{Z}^n_2\) by using the tensor product of \(n\) copies of the Neveu-Schwarz vertex operator superalgebra \(M=L({1\over2},0)\oplus L({1\over2},{1\over2})\). It is proved that if \(D\) has no words of weight 2, then \((M_D)_1=0\), i.e. there are no nonzero vectors of weight 1, and the full automorphism group of \(M_D\) is finite. Moreover, if \(D\) contains an \([8,4,4]\) Hamming subcode \(C\), then \(C\) defines a nontrivial involutive automorphism of \(M_D\) which is not induced from the automorphism group of \(D\). Some of the proofs rely on results in [\textit{M. Miyamoto}, Griess algebras and conformal vectors in vertex operator algebras, J. Algebra 179, No. 2, 523-548 (1996; Zbl 0964.17021)].
reviewed by: Mirko Primc
Mathematics Subject Classification ID: 17B69
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 17B70
zbMATH DE Number: 883756
zbMATH Keywords: vertex operator algebras
zbMATH Keywords: Virasoro element
zbMATH Keywords: conformal vectors
zbMATH Keywords: moonshine module
zbMATH Keywords: even binary code
zbMATH Keywords: Hamming subcode
zbMATH Keywords: automorphism
MaRDI profile type: Publication
full work available at URL: jabr.1996.0116
OpenAlex ID: W1982578719
DOI: 10.1006/JABR.1996.0116
description: scientific article; zbMATH DE number 883756