Commutative post-Lie algebra structures on Lie algebras

TL;DR

This paper investigates commutative post-Lie algebra structures on Lie algebras, proving triviality on perfect Lie algebras, decomposing inner structures, and classifying CPA-structures on parabolic subalgebras of simple Lie algebras.

Contribution

It provides a classification of CPA-structures on certain Lie algebras and shows their triviality on perfect Lie algebras, advancing understanding of algebraic structures.

Findings

CPA-structures on perfect Lie algebras are trivial

Inner CPA-structures can be decomposed systematically

Complete classification of CPA-structures on parabolic subalgebras

Abstract

We show that any CPA-structure (commutative post-Lie algebra structure) on a perfect Lie algebra is trivial. Furthermore we give a general decomposition of inner CPA-structures, and classify all CPA-structures on parabolic subalgebras of simple Lie algebras.