Inner post-Lie algebras and inner post-groups

TL;DR

This paper introduces the concept of obstruction classes for inner post-Lie algebras and groups induced by Rota-Baxter operators, providing criteria for their induction and exploring applications.

Contribution

It develops a cohomological framework to characterize when inner post-Lie algebras and groups are induced by Rota-Baxter operators, including new obstruction classes and their triviality conditions.

Findings

Obstruction classes determine when inner post-Lie algebras are induced by Rota-Baxter operators.

Parallel results are established for inner post-groups.

Applications of the theory are demonstrated.

Abstract

In this paper, using extension theory and cohomological approach we introduce the notion of the obstruction class for an inner post-Lie algebra being induced by a Rota-Baxter operator, and show that an inner post-Lie algebra is induced by a Rota-Baxter operator if and only if the obstruction class is trivial. Similarly, we introduce the notion of the obstruction class for an inner post-group being induced by a Rota-Baxter operator, and prove a parallel result. Finally, we give some applications of inner post-Lie algebras and inner post-groups.