Baxter Algebras and Differential Algebras

Details Baxter Algebras and Differential Algebras Baxter Algebras and Differential Algebras

2004-07-10

arxiv.org/abs/math/0407180v1

Differential Algebra and Related Topics, World Scientific Publishing Company, 2002, 281-305

Mathematics

Rings and Algebras

24 pages

Scientific paper

A Baxter algebra is a commutative algebra $A$ that carries a generalized integral operator. In the first part of this paper we review past work of Baxter, Miller, Rota and Cartier in this area and explain more recent work on explicit constructions of free Baxter algebras that extended the constructions of Rota and Cartier. In the second part of the paper we will use these explicit constructions to relate Baxter algebras to Hopf algebras and give applications of Baxter algebras to the umbral calculus in combinatorics.

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