About some varieties of Leibnitz algebras

TL;DR

This paper introduces new findings on varieties of Leibnitz algebras, including examples of non-nilpotent varieties satisfying Engel conditions in prime characteristic and results on multilinear elements in zero characteristic.

Contribution

It provides novel examples and theoretical results on Leibnitz algebra varieties, expanding understanding in both prime and zero characteristic cases.

Findings

Constructed non-nilpotent Leibnitz varieties satisfying Engel conditions in characteristic p.

Obtained results on the space of multilinear elements in left nilpotent Leibnitz algebras.

Analyzed varieties of Leibnitz algebras with specific nilpotency classes.

Abstract

The paper presents two new results concerning the varieties of Leibnitz algebras. In the case of prime characteristic p of the base field constructed example not nilpotent variety of Leibnitz algebras satisfying an Engel condition order p. In the case of zero characteristic obtained new results concerning the space of multilinear elements variety of left nilpotent of the class not more than 3 Leibnitz algebras.