Akivis superalgebras and speciality

Abstract

In this paper we define Akivis superalgebra and study enveloping superalgebras for this class of algebras, proving an analogous of the PBW Theorem. Lie and Malcev superalgebras are examples of Akivis superalgebras. For these particular superalgebras, we describe the connection between the classical enveloping superalgebras and the corresponding generalized concept defined in this work.