Simple and prime graded Jordan algebras
type: Item
instance of: scholarly article
title: Simple and prime graded Jordan algebras
zbMATH Open document ID: 0885.17023
published in: Journal of Algebra
publication date: 1998-04-05T00:00:00Z
review text: By a theorem of \textit{O. Mathieu} [Invent. Math. 108, 455-519 (1992; Zbl 0769.17018)] it is known that the infinite dimensional simple graded Lie algebras of finite growth are either loop algebras, algebras of Cartan type or the Virasoro algebra. The paper under review deals with the same problem for Jordan algebras. The graded simple infinite dimensional Jordan algebras of finite growth (over an algebraically closed field of characteristic 0) are shown to be either loop algebras or Jordan algebras of a symmetric bilinear form. Moreover, the graded prime and nondegenerate Jordan algebras with the more restrictive condition of being of growth 1 (that is, the dimension of the homogeneous components is bounded) are proved to be either graded simple or related to loop algebras in a specific way.
Mathematics Subject Classification ID: 17C20
zbMATH DE Number: 1066139
zbMATH Keywords: graded prime Jordan algebra
zbMATH Keywords: finite growth
zbMATH Keywords: graded simple Jordan algebra
zbMATH Keywords: infinite dimensional Jordan algebras of finite growth
author: Consuelo Martínez
author: E. Zelmanov
reviewed by: Alberto Elduque
MaRDI profile type: Publication
full work available at URL: jabr.1996.6960
OpenAlex ID: W2059219878
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DOI: 10.1006/JABR.1996.6960
description: scientific article; zbMATH DE number 1066139