Rota-Baxter Operators on Cocommutative Weak Hopf Algebras

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 HB=(H,*,eta,& UDelta;,epsilon,S-B) becomes a new weak Hopf algebra. Finally, all Rota-Baxter operators on a weak Hopf algebra of a matrix algebra are given.