Structure theorems of mixable shuffle algebras and free commutative Rota-Baxter algebras

Details Structure theorems of mixable shuffle algebras and free commutative Rota-Baxter algebras Structure theorems of mixable shuffle algebras and free commutative Rota-Baxter algebras

2008-07-14

arxiv.org/abs/0807.2267v2

Mathematics

Rings and Algebras

30 pages. Corrected typos and improved presentation

Scientific paper

We study the ring theoretical structures of mixable shuffle algebras and their associated free commutative Rota-Baxter algebras. For this study we utilize the connection of the mixable shuffle algebras with the overlapping shuffle algebra of Hazewinkel, quasi-shuffle algebras of Hoffman and quasi-symmetric functions. This connection allows us to apply methods and results on shuffle products and Lyndon words on ordered sets. As a result, we obtain structure theorems for a large class of mixable shuffle algebras and free commutative Rota-Baxter algebras with various coefficient rings.

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