On Free Baxter Algebras: Completions and the Internal Construction

Details On Free Baxter Algebras: Completions and the Internal Construction On Free Baxter Algebras: Completions and the Internal Construction

2004-07-09

arxiv.org/abs/math/0407156v1

Advances in Math, 151 (2000), 101-127

Mathematics

Rings and Algebras

25 pages

Scientific paper

We continue the study of free Baxter algebras. There are two goals of this paper. The first goal is to extend the construction of shuffle Baxter algebras to completions of Baxter algebras. This process is motivated by a construction of Cartier and is analogous to the process of completing a polynomial algebra to obtain a power series algebra. However, as we will see later, unlike the close similarity of properties of a polynomial algebra and a power series algebra, properties of a shuffle Baxter algebra and its completion can be quite different.

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