FREE MODIFIED ROTA-BAXTER ALGEBRAS AND HOPF ALGEBRAS

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International Electronic Journal of Algebra
Volume:25 Issue:25
FREE MODIFIED ROTA-BAXTER ALGEBRAS AND HOPF ALGEBRAS

FREE MODIFIED ROTA-BAXTER ALGEBRAS AND HOPF ALGEBRAS

Authors : Xigou ZHANG, Xing GAO, Li GUO

Pages : 12-34

Doi:10.24330/ieja.504101

View : 14 | Download : 10

Publication Date : 2019-01-08

Article Type : Research Paper

Abstract :The notion of a modi ed Rota-Baxter algebra comes from the combination of those of a Rota-Baxter algebra and a modi ed Yang-Baxter equation. In this paper, we rst construct free modi ed Rota-Baxter algebras. We then equip a free modi ed 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 modi ed Rota-Baxter alge- bra with a Hopf algebra structure.
Keywords : Modi ed Rota Baxter algebra, Rota Baxter algebra, Hopf algebra, bracketed word, cocycle

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