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 SB from a Rota–Baxter operator B on H such that HB=(H,∗,η,Δ,ε,SB) becomes a new weak Hopf algebra. Finally, all Rota–Baxter operators on a weak Hopf algebra of a matrix algebra are given.
Highlights
Introduction and PreliminariesCitation: Wang, Z.; Guan, Z.; Zhang, Y.; Zhang, L
We introduce and study Rota–Baxter operators on cocommutative weak Hopf algebras, which is the motivation of this paper
We present some examples of Rota–Baxter weak Hopf algebras
Summary
For this purpose, we introduce and study Rota–Baxter operators on cocommutative weak Hopf algebras, which is the motivation of this paper. Rota–Baxter operator on a cocommutative weak Hopf algebra and investigate its properties. We construct Rota–Baxter operators by using the normalized integral, antipode, and target map of weak Hopf algebras, respectively. The groupoid algebra KG (generated by morphisms in G with the product of two morphisms being equal to their composition if the latter is defined and 0 otherwise) is a quantum groupoid (weak Hopf algebra) in [18] via.
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