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On Differential Rota-Baxter Algebras
Li Guo, William Keigher
A Rota-Baxter operator of weight is an abstraction of both the integral operator (when ) and the summation operator (when ). We similarly define a differential operat…
Baxter Algebras and Hopf Algebras
George E. Andrews, Li Guo, William Keigher +1
By applying a recent construction of free Baxter algebras, we obtain a new class of Hopf algebras that generalizes the classical divided power Hopf algebra. We also study condition…
On Free Baxter Algebras: Completions and the Internal Construction
Li Guo, William Keigher
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 a…
Baxter Algebras and Shuffle Products
Li Guo, William Keigher
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 shu…