Restricted Lie algebras via monadic decomposition

TL;DR

This paper characterizes the category of restricted Lie algebras over a field of prime characteristic using monadic decomposition of a functor related to primitive elements in bialgebras.

Contribution

It introduces a novel approach to describe restricted Lie algebras through monadic decomposition, linking them to primitive elements in bialgebras.

Findings

Provides a categorical description of restricted Lie algebras

Connects primitive elements in bialgebras to restricted Lie algebra structure

Uses monadic decomposition to analyze algebraic structures

Abstract

We give a description of the category of restricted Lie algebras over a field $\Bbbk $ of prime characteristic by means of monadic decomposition of the functor that computes the $\Bbbk $-vector space of primitive elements of a $\Bbbk $-bialgebra.