Nilpotent symplectic alternating algebras. I
type: Item
instance of: scholarly article
title: Nilpotent symplectic alternating algebras. I
zbMATH Open document ID: 1369.17032
author: Layla Sorkatti
author: Gunnar Traustason
published in: Journal of Algebra
publication date: 2014-12-05T00:00:00Z
review text: A symplectic alternating algebra over a field is a anticommutative algebra equipped with a non-degenerate alternating form, such that \((uv,w)=(vw,u)\) for all \(u,v,w\in L\). These algebras were introduced by \textit{P. Moravec} and \textit{G. Traustason} in the study of 2-Engel groups [Commun. Algebra 36, No. 11, 4096--4119 (2008; Zbl 1159.20017)]. The present paper studies these algebras that are nilpotent. Various structural properties are shown. For example, these algebras admit an increasing chain of isotropic ideals, each of codimension one in the next. The algebras of maximal class are investigated. The classification of these algebras of dimension up to eight is given. The authors extend [Int. J. Algebra Comput. 26, No. 5, 1071--1094 (2016; Zbl 1369.17033); ibid. 26, No. 5, 1095--1124 (2016; Zbl 1369.17034)] the classification to dimension ten.
Mathematics Subject Classification ID: 17D99
zbMATH DE Number: 6377591
zbMATH Keywords: non-associative algebras
zbMATH Keywords: symplectic
zbMATH Keywords: nilpotent
zbMATH Keywords: classification
reviewed by: Ernest L. Stitzinger
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2014.10.031
OpenAlex ID: W2043423518
cites work: Alternating trilinear forms and groups of exponent 6
cites work: Powerful 2-Engel Groups
cites work: Symplectic alternating nil-algebras
cites work: Powerful 2-Engel groups. II.
cites work: SYMPLECTIC ALTERNATING ALGEBRAS
DOI: 10.1016/J.JALGEBRA.2014.10.031
description: scientific article; zbMATH DE number 6377591