On classification of $7$-dimensional odd-nilpotent Leibniz algebras

Year 2024, Volume: 53 Issue: 1, 121 - 129, 29.02.2024

İsmail Demir

https://doi.org/10.15672/hujms.1185538

https://izlik.org/JA44FC95AA

Abstract

In this paper we extend the method of canonical form for congruence of bilinear forms to give the classification of some subclasses of $7-$dimensional nilpotent Leibniz algebras. Odd-nilpotent Leibniz algebras are defined as that its even dimensional ideals in lower central series are all zero and the classification of $7-$dimensional complex odd-nilpotent Leibniz algebras with one dimensional Leib ideal is obtained by applying the aforementioned method.

Keywords

Leibniz algebra , nilpotency , classification

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