Modified Rota–Baxter Algebras, Shuffle Products and Hopf Algebras

Abstract

In this paper, we begin a systematic study of modified Rota–Baxter algebras, as an associative analogue of the modified classical Yang–Baxter equation. We construct free commutative modified Rota–Baxter algebras by a variation of the shuffle product and describe the structure both recursively and explicitly. We then provide these algebras with a Hopf algebra structure by applying a Hochschild cocycle.