Yetter-Drinfel'd algebras and coideals of Weak Hopf $C^*$-Algebras

Abstract

We characterize braided commutative Yetter-Drinfeld C * -algebras over weak Hopf C * -algebras in categorical terms. Using this, we then study quotient type coideal subalgebras of a given weak Hopf C *algebra G and coideal subalgebras invariant with respect to the adjoint action of G. Finally, as an example, we explicitly describe quotient type coideal subalgebras of the weak Hopf C * -algebras associated with Tambara-Yamagami categories.