Loday-type Algebras and the Rota-Baxter Relation

TL;DR

This paper explores the connection between Rota-Baxter operators and Loday-type algebras, demonstrating that associative algebras with Rota-Baxter operators naturally induce dendriform structures, revealing a fundamental algebraic relationship.

Contribution

It establishes that any associative algebra with a Rota-Baxter operator of any weight inherently possesses a dendriform algebra structure, linking these algebraic concepts.

Findings

Associative algebras with Rota-Baxter operators induce dendriform structures.

The relation holds for Rota-Baxter operators of arbitrary weight.

Provides insight into the algebraic structure linking Rota-Baxter operators and Loday-type algebras.

Abstract

In this brief note we would like to report on an observation concerning the relation between Rota-Baxter operators and Loday-type algebras, i.e. dendriform di- and trialgebras. It is shown that associative algebras equipped with a Rota-Baxter operator of arbitrary weight always give such dendriform structures.