Bernstein algebras given by symmetric bilinear forms
type: Item
instance of: scholarly article
title: Bernstein algebras given by symmetric bilinear forms
zbMATH Open document ID: 0723.17029
DOI: 10.1016/0024-3795(91)90297-A
author: Irvin Roy Hentzel
author: Luiz Antonio Peresi
published in: Linear Algebra and its Applications
publication date: 1991-01-01T00:00:00Z
review text: Let (A,\(\omega\)) be a finite dimensional Bernstein algebra and N the kernel of \(\omega\). The authors study these algebras when dim \(N_ 2\) is 1. Let e be an idempotent of A, Z the kernel of \(R_ e\), U the kernel of \(2R_ e-I\). There are two possibilities: \(N^ 2\subseteq Z\), or \(N^ 2\subseteq U.\) The first case is completely classified. In the second case, it is shown that A is a subalgebra of a complete algebra (whose definition is given). In the last part, the authors consider a real Bernstein algebra such that dim \(N^ 2\) is 1; they prove a necessary and sufficient condition for A to be a Jordan algebra.
Mathematics Subject Classification ID: 17D92
zbMATH DE Number: 4191960
zbMATH Keywords: multiplication tables
zbMATH Keywords: complete algebra
zbMATH Keywords: kernel
zbMATH Keywords: symmetric bilinear forms
zbMATH Keywords: Jordan Bernstein algebras
reviewed by: Monique Bertrand
MaRDI profile type: Publication
cites work: Q5614003
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description: scientific article; zbMATH DE number 4191960