Multipliers and Unicentral Leibniz Algebras

2021/06/24 by Mainellis, Erik
#17A32 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2106.13294

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.

Related

• The Schur Lie-Multiplier of Leibinz Algebras
• The c-Nilpotent Shur Lie-Multiplier of Leibniz Algebras
• Multipliers and Unicentral Diassociative Algebras
• Remarks on Leibniz algebras
• On the Schur Lie-multiplier and Lie-covers of Leibniz n-algebras