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july 2020 Left counital Hopf algebras on bi-decorated planar rooted forests and Rota-Baxter systems
Xiao-Song Peng, Yi Zhang, Xing Gao, Yan-Feng Luo
Bull. Belg. Math. Soc. Simon Stevin 27(2): 219-243 (july 2020). DOI: 10.36045/bbms/1594346416

Abstract

Involving an extended 1-cocycle condition, we first define a coproduct on the space of bi-decorated planar rooted forests to equip it with a left counital bialgebraic structure. We introduce the concept of left counital $(\Omega, \alpha)$-cocyle bialgebras and show that the space of bi-decorated planar rooted forests is the free object in the category of left counital $(\Omega, \alpha)$-cocyle bialgebras. We then prove a generalized fact that a connected graded left counital bialgebra is a left counital right antipode Hopf algebra in the sense that the antipode is only right-sided. Having this fact in hand, a left counital Hopf algebraic structure on bi-decorated rooted forests is also established. Finally, we construct a Rota-Baxter system on the left counital Hopf algebra.

Citation

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Xiao-Song Peng. Yi Zhang. Xing Gao. Yan-Feng Luo. "Left counital Hopf algebras on bi-decorated planar rooted forests and Rota-Baxter systems." Bull. Belg. Math. Soc. Simon Stevin 27 (2) 219 - 243, july 2020. https://doi.org/10.36045/bbms/1594346416

Information

Published: july 2020
First available in Project Euclid: 10 July 2020

zbMATH: 07242767
MathSciNet: MR4121372
Digital Object Identifier: 10.36045/bbms/1594346416

Subjects:
Primary: 16S10, 16T10, 16T30, 16W99, 81R15

Rights: Copyright © 2020 The Belgian Mathematical Society

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Vol.27 • No. 2 • july 2020
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