Classification of five-dimensional nilpotent Jordan algebras
Rings and Algebras
2016-01-21 v2 Mathematical Physics
Commutative Algebra
math.MP
Abstract
The paper is devoted to classify nilpotent Jordan algebras of dimension up to five over an algebraically closed field of characteristic not 2. We obtained a list of 35 isolated non-isomorphic 5-dimensional nilpotent non-associative Jordan algebras and 6 families of non-isomorphic 5-dimensional nilpotent non-associative Jordan algebras depending either on one or two parameters over an algebraically closed field of characteristic not 2 or 3. In addition to these algebras we obtained two non-isomorphic 5-dimensional nilpotent non-associative Jordan algebras over an algebraically closed field of characteristic 3.
Cite
@article{arxiv.1401.3992,
title = {Classification of five-dimensional nilpotent Jordan algebras},
author = {A. S. Hegazi and Hani Abdelwahab},
journal= {arXiv preprint arXiv:1401.3992},
year = {2016}
}