Baxter Algebras and Shuffle Products

Mathematics – Rings and Algebras

Scientific paper

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30 pages

Scientific paper

In this paper we generalize the well-known construction of shuffle product
algebras by using mixable shuffles, and prove that any free Baxter algebra is
isomorphic to a mixable shuffle product algebra. This gives an explicit
construction of the free Baxter algebra, extending the work of Rota and
Cartier.

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