On equivariant dendriform algebras

TL;DR

This paper explores how finite group actions influence dendriform algebras, introducing equivariant cohomology and demonstrating its role in controlling formal deformations of these algebraic structures.

Contribution

It defines equivariant cohomology for dendriform algebras with finite group actions and links it to deformation theory, extending the understanding of symmetry in algebraic deformations.

Findings

Introduces equivariant cohomology for dendriform algebras with group actions

Shows equivariant cohomology controls algebra deformations

Establishes parallels with Bredon cohomology in topology

Abstract

Dendriform algebras are certain associative algebras whose product splits into two binary operations and the associativity splits into three new identities. In this paper, we study finite group actions on dendriform algebras. We define equivariant cohomology for dendriform algebras equipped with finite group actions similar to the Bredon cohomology for topological $G$-spaces. We show that equivariant cohomology of such dendriform algebras controls equivariant one-parameter formal deformations.