Nilpotent symplectic alternating algebras. I
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.
scientific article; zbMATH DE number 6377591