Hopf and Lie algebras in semi-additive Varieties

TL;DR

This paper explores the structure of Hopf monoids within semi-additive varieties, focusing on adjunctions related to enveloping and primitive element functors, and introduces the concept of the abelian core in this context.

Contribution

It introduces the concept of the abelian core of a semi-additive variety and analyzes its monoidal structure in entropic cases, advancing understanding of Hopf monoids in these settings.

Findings

Characterization of the abelian core in semi-additive varieties

Analysis of adjunctions involving enveloping and primitive functors

Insights into the monoidal structure of the abelian core in entropic varieties

Abstract

We study Hopf monoids in entropic semi-additive varieties with an emphasis on adjunctions related to the enveloping monoid functor and the primitive element functor. These investigations are based on the concept of the abelian core of a semi-additive variety variety and its monoidal structure in case the variety is entropic.