Cohomology and deformations of hom-dendriform algebras and coalgebras

TL;DR

This paper develops a cohomology theory and studies deformations for hom-dendriform algebras and coalgebras, linking them to Hochschild-type cohomology of hom-associative algebras, expanding the understanding of their algebraic structures.

Contribution

It introduces a cohomology framework for hom-dendriform algebras and coalgebras, connecting it to existing Hochschild-type cohomology, and explores their deformation theory.

Findings

Defined cohomology for hom-dendriform algebras

Related cohomology to Hochschild-type cohomology

Extended results to hom-dendriform coalgebras

Abstract

Hom-dendriform algebras are twisted analog of dendriform algebras and are splitting of hom-associative algebras. In this paper, we define a cohomology and deformation for hom-dendriform algebras. We relate this cohomology with the Hochschild-type cohomology of hom-associative algebras. We also describe similar results for the twisted analog of dendriform coalgebras.