On a class of power-associative algebras
type: Item
instance of: scholarly article
title: On a class of power-associative algebras
zbMATH Open document ID: 0856.17001
DOI: 10.1016/0024-3795(94)00113-8
author: Moussa Ouattara
published in: Linear Algebra and its Applications
publication date: 1996-06-10T00:00:00Z
review text: This paper is about finite-dimensional, commutative, power-associative algebras \(A\) over a field \(K\) of characteristic \(\neq 2\) which have an idempotent \(e\) such that the associated Peirce decomposition \(A=A_0 + A_{1/2} + A_1\) satisfies \(\dim (A_1)=1\) or \(A_0 = \{0\}\). It follows from an earlier result of the author that such algebras are train algebras. The algebras in the first class are shown to be Bernstein algebras of some order \(n\) provided they are Jordan. Conversely, any power-associative \(n\)-th order Bernstein algebra is contained in this class. The Jordan algebras in the second class are shown to admit a train equation \((L(x)-\omega (x) \text{id})^m(x) = 0\) for some \(m\).
Mathematics Subject Classification ID: 17A05
Mathematics Subject Classification ID: 17D92
Mathematics Subject Classification ID: 17C05
zbMATH DE Number: 871110
zbMATH Keywords: power-associative algebras
zbMATH Keywords: idempotent
zbMATH Keywords: Peirce decomposition
zbMATH Keywords: train algebras
zbMATH Keywords: Bernstein algebras
zbMATH Keywords: Jordan algebras
reviewed by: S Walcher
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00113-8
OpenAlex ID: W1986875975
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description: scientific article; zbMATH DE number 871110