Coordinate algebras of extended affine Lie algebras of type \(A_1\)
type: Item
instance of: scholarly article
title: Coordinate algebras of extended affine Lie algebras of type \(A_1\)
zbMATH Open document ID: 0974.17026
author: Yoji Yoshii
published in: Journal of Algebra
publication date: 2001-12-13T00:00:00Z
review text: The cores of extended affine Lie algebras of reduced types were classified except for type \(A_1\) [cf. \textit{S. Berman, Y. Gao} and \textit{Y. Krylyuk}, J. Funct. Anal. 135, 339-389 (1996; Zbl 0847.17009)]. In this paper the author first shows that the core of any extended affine Lie algebra of type \(A_1\) is a central extension of a Lie algebra \(\text{TKK} (J)\) (obtained from a Jordan algebra \(J\) by the Tits-Kantor-Koecher construction), where the so-called coordinate algebra \(J\) is a unital \(\mathbb Z^n\)-graded Jordan algebra of certain type, called a Jordan torus. The major part of the paper is devoted to a classification of Jordan tori (over any field of characteristic \(\neq 2\)) into five classes. In particular, a Jordan torus is either of Hermitian, Clifford, or Albert type, and for each type the author determines the possible Jordan tori.
reviewed by: Mirko Primc
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 17C50
zbMATH DE Number: 1565856
zbMATH Keywords: core
zbMATH Keywords: extended affine Lie algebra of type \(A_1\)
zbMATH Keywords: central extension
zbMATH Keywords: Tits-Kantor-Koecher construction
zbMATH Keywords: Jordan torus
MaRDI profile type: Publication
full work available at URL: jabr.2000.8450
OpenAlex ID: W2057739778
Wikidata QID: Q115395758
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DOI: 10.1006/JABR.2000.8450
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description: scientific article; zbMATH DE number 1565856