Mixable Shuffles, Quasi-shuffles and Hopf Algebras

Abstract

The quasi-shuffle product and mixable shuffle product are both generalizations of the shuffle product and have both been studied quite extensively recently. We relate these two generalizations and realize quasi-shuffle product algebras as subalgebras of mixable shuffle product algebras. As an application, we obtain Hopf algebra structures in free Rota-Baxter algebras.

14 pages, no figure, references updated

References in corpus (3)

• Loday-type Algebras and the Rota-Baxter Relation
• Spitzer's Identity and the Algebraic Birkhoff Decomposition in pQFT
• On Products and Duality of Binary, Quadratic, Regular Operads

Cited by in corpus (6)

• On Products and Duality of Binary, Quadratic, Regular Operads
• Generalized shuffles related to Nijenhuis and TD-algebras
• Differential Birkhoff decomposition and the renormalization of multiple zeta values
• Hopf algebras in dynamical systems theory
• Structure theorems of mixable shuffle algebras and free commutative Rota-Baxter algebras
• Universal enveloping commutative Rota-Baxter algebras of precommutative and postcommutative algebras