Rota-Baxter Hom-Lie-admissible algebras

TL;DR

This paper introduces Hom-type analogs of Rota-Baxter and dendriform algebras, providing new constructions, free algebra models, and functorial relationships between these algebraic structures.

Contribution

It develops the theory of Rota-Baxter G-Hom-associative and Hom-dendriform algebras, including explicit free constructions and categorical adjunctions.

Findings

Constructed free algebras for the new structures

Established functors between categories of these algebras

Proved adjunctions linking Rota-Baxter Hom-associative and Hom-dendriform algebras

Abstract

We study Hom-type analogs of Rota-Baxter and dendriform algebras, called Rota-Baxter $G$-Hom-associative algebras and Hom-dendriform algebras. Several construction results are proved. Free algebras for these objects are explicitly constructed. Various functors between these categories, as well as an adjunction between the categories of Rota-Baxter Hom-associative algebras and of Hom-(tri)dendriform algebras, are constructed.