Akivis Superalgebras and speciality

TL;DR

This paper introduces Akivis superalgebras, explores their enveloping structures, and proves a PBW-type theorem, connecting classical Lie and Malcev superalgebras to this new framework.

Contribution

It defines Akivis superalgebras, develops their enveloping superalgebras, and establishes a PBW theorem, extending classical algebraic concepts to this new class.

Findings

Akivis superalgebras generalize Lie and Malcev superalgebras.

A PBW-type theorem is proved for Akivis superalgebras.

Connections between classical and generalized enveloping superalgebras are described.

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.