Multipliers and Unicentral Leibniz Algebras

TL;DR

This paper extends Lie algebra results to Leibniz algebras, focusing on multipliers, centers, and cohomology, and introduces the concept of unicentral Leibniz algebras with new theoretical insights.

Contribution

It generalizes Lie algebra results to Leibniz algebras, characterizes multipliers via cohomology, and develops the theory of unicentral Leibniz algebras.

Findings

Multiplier characterized by second cohomology group

Criteria for center mappings in covers

Introduction of unicentral Leibniz algebras

Abstract

This paper details the Leibniz generalization of Lie-theoretic results from Peggy Batten's 1993 dissertation. We first show that the multiplier of a Leibniz algebra is characterized by its second cohomology group with coefficients in the field. We then establish criteria for when the center of a cover maps onto the center of the algebra. Along the way, we obtain a collection of exact sequences and a brief theory of unicentral Leibniz algebras.