Classification of five-dimensional nilpotent Jordan algebras

The paper is devoted to classify nilpotent Jordan algebras of dimension up to five over an algebraically closed field F 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 nil...

Full description

Saved in:
Bibliographic Details
Published in:Linear algebra and its applications 2016-04, Vol.494, p.165-218
Main Authors: Hegazi, A.S., Abdelwahab, Hani
Format: Article
Language:English
Subjects:
Annihilator extension
Automorphism group
Nilpotent Jordan algebras
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The paper is devoted to classify nilpotent Jordan algebras of dimension up to five over an algebraically closed field F 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 ≠2,3. 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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2016.01.015