On regular Bernstein algebras
type: Item
instance of: scholarly article
title: On regular Bernstein algebras
zbMATH Open document ID: 0878.17034
DOI: 10.1016/0024-3795(95)00589-7
author: Consuelo Martínez
author: Santos González
author: J. Carlos Gutiérrez
published in: Linear Algebra and its Applications
publication date: 1996-11-25T00:00:00Z
review text: Given a Bernstein algebra which is regular (that is, \(AV=0\), where \(V\) is the null Peirce space relative to any idempotent) and nuclear (\(A^2=A\)), and once an idempotent is fixed, the algebra is determined by an onto linear map \(S^2(U)\to V\), where \(U\) is the one-half Peirce component and \(S^2(U)\) the space of symmetric tensors on \(U\) of degree 2. The authors then look at both the kernel and image of this map to get isomorphism conditions between two of these algebras. This allows them to classify the regular nuclear Bernstein algebras of types \((n+1,1)\) and \((n+1,n(n+1)/2-1)\) over the real and complex fields. Finally, the real regular nuclear Bernstein algebras of type \((n+1,1)\) with a so called stochastic realization are determined too.
reviewed by: Alberto Elduque
Mathematics Subject Classification ID: 17D92
zbMATH DE Number: 931896
zbMATH Keywords: stochastic realization
zbMATH Keywords: regular nuclear Bernstein algebras
MaRDI profile type: Publication
full work available at URL: 0024-3795(95)00589-7
OpenAlex ID: W2050425983
cites work: Q4050426
cites work: TWO-LEVEL BERNSTEINIAN POPULATIONS
cites work: Q4182313
cites work: Q3752547
cites work: Q4283475
cites work: Q3724143
description: scientific article; zbMATH DE number 931896