On train algebras of rank 3
type: Item
instance of: scholarly article
title: On train algebras of rank 3
zbMATH Open document ID: 0728.17019
DOI: 10.1016/0024-3795(91)90081-7
author: N. E. Zubov
published in: Linear Algebra and its Applications
publication date: 1991-01-01T00:00:00Z
review text: First, the author recalls some concepts introduced in his preceding paper [cf. Proc. Edinb. Math. Soc., II. Ser. 33, No.1, 61-70 (1990; Zbl 0671.17022)]: train algebras of rank 3, the type of such algebras, which is an ordered pair of integers. In section 1 all train algebras of type (n,1) are classified such that dim J\(=\dim B_ 1B_ 2\oplus B_ 2\geq 2\). In section 2 train algebras of type (3,n-2) such that dim J\(=n-1\) are classified. In section 3 all train algebras \(B'\) are considered whose kernel B is anisotropic, that is to say that dim \(B^ 2=1\) and the bilinear form defined by the multiplication has a one-dimensional radical and its regular part is anisotropic.
Mathematics Subject Classification ID: 17D92
zbMATH DE Number: 4202539
zbMATH Keywords: genetic algebra
zbMATH Keywords: anisotropic kernel
zbMATH Keywords: train algebras
reviewed by: Monique Bertrand
MaRDI profile type: Publication
full work available at URL: 0024-3795(91)90081-7
OpenAlex ID: W1993288486
cites work: Principal train algebras of rank 3 and dimensions≦5
cites work: Q3869125
description: scientific article; zbMATH DE number 4202539