Rota–Baxter Operators on Cocommutative Weak Hopf Algebras

Zhongwei Wang, Zhen Guan, Yi Zhang and Liangyun Zhang
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Zhongwei Wang: School of Mathematics, Southeast University, Nanjing 211189, China
Zhen Guan: Department of Mathematics, Nanjing Agricultural University, Nanjing 210095, China
Yi Zhang: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
Liangyun Zhang: Department of Mathematics, Nanjing Agricultural University, Nanjing 210095, China

Mathematics, 2021, vol. 10, issue 1, 1-14

Abstract: In this paper, we first introduce the concept of a Rota–Baxter operator on a cocommutative weak Hopf algebra H and give some examples. We then construct Rota–Baxter operators from the normalized integral, antipode, and target map of H . Moreover, we construct a new multiplication “∗” and an antipode S B from a Rota–Baxter operator B on H such that H B = ( H , ∗ , η , Δ , ε , S B ) becomes a new weak Hopf algebra. Finally, all Rota–Baxter operators on a weak Hopf algebra of a matrix algebra are given.

Keywords: weak Hopf algebra; Rota–Baxter operator; normalized integral; matrix algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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