The Structure of Digroups

Abstract

A digroup is an algebra defined on a set having two associative binary operations, ⊢ and ⊣. Digroups play an important role in an open problem in the theory of Leibniz algebras. We present a brief overview of digroups and a set of more general axioms for a digroup than used previously. We then consider several properties of a digroup having distinct elements a and b such that a ⊢ b = b ⊢ a, but a ⊢ b ≠ a ⊣ b.