Universal enveloping algebras for Malcev color algebras

TL;DR

This paper constructs universal enveloping algebras for Malcev algebras within categories of group algebra comodules, including super vector spaces, using bicharacter symmetries.

Contribution

It introduces a new construction of universal enveloping algebras for Malcev algebras in symmetric monoidal categories defined by bicharacters.

Findings

Provides a construction applicable to super vector spaces.

Extends the theory of Malcev algebras to new categorical contexts.

Lays groundwork for further algebraic and categorical studies.

Abstract

In this paper we give a construction of the universal enveloping algebra of a Malcev algebra in categories of group algebra comodules with a symmetry given by a bicharacter of the group. A particular example of such categories is the category of super vector spaces.