Classification of division \({\mathbb Z}^n\)-graded alternative algebras.
type: Item
instance of: scholarly article
title: Classification of division \({\mathbb Z}^n\)-graded alternative algebras.
zbMATH Open document ID: 1068.17012
DOI: 10.1016/S0021-8693(02)00022-4
author: Yoji Yoshii
published in: Journal of Algebra
publication date: 2003-02-12T00:00:00Z
review text: The octonion torus appears as a coordinate algebra of extended affine Lie algebras of type \(A_2\) and \(F_4\). The author classifies a generalized version of the octonion torus, called division \(\mathbb Z^n\)-graded alternative algebras. It turns out that they are strongly prime and so by a result due to Slater it is either associative or an octonion ring, i. e., its central closure is an octonion algebra. The author identifies four specific division \(\mathbb Z^n\)-graded octonion rings, and he obtains that a division \(\mathbb Z^n\)-graded octonion ring is isomorphic to exactly one of these. Using this result, the author completes the classification of division \((A_2,\mathbb Z^n)\)-graded Lie algebras, up to central extensions, which are a generalization of the cores of extended affine Lie algebras of type \(A_2\).
Mathematics Subject Classification ID: 17D05
zbMATH DE Number: 1868019
zbMATH Keywords: alternative algebra
zbMATH Keywords: octonion ring
zbMATH Keywords: division \(\mathbb Z^n\)-graded alternative algebra
reviewed by: María Concepción López-Díaz
MaRDI profile type: Publication
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full work available at URL: s0021-8693(02)00022-4
OpenAlex ID: W2085231713
description: scientific article; zbMATH DE number 1868019