Multipliers and Unicentral Leibniz Algebras

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.