Title of article :
FREE MODIFIED ROTA-BAXTER ALGEBRAS and HOPF ALGEBRAS
Author/Authors :
Zhang, Xigou College of Mathematics and Information Science - Jiangxi Normal University, China , Gao, Xing School of Mathematics and Statistics - Key Laboratory of Applied Mathematics and Complex Systems - Lanzhou University, china , Guo, Li Department of Mathematics and Computer Science - Rutgers University - Newark, USA
Abstract :
The notion of a modified Rota-Baxter algebra comes from the
combination of those of a Rota-Baxter algebra and a modified Yang-Baxter
equation. In this paper, we first construct free modified Rota-Baxter algebras.
We then equip a free modified Rota-Baxter algebra with a bialgebra structure
by a cocycle construction. Under the assumption that the generating algebra
is a connected bialgebra, we further equip the free modified Rota-Baxter algebra with a Hopf algebra structure.
Keywords :
Modified Rota-Baxter algebra , Rota-Baxter algebra , Hopf algebra , bracketed word , cocycle
Journal title :
International Electronic Journal of Algebra
