We characterize braided commutative Yetter-Drinfel'd 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.
Keywords: Coactions and corepresentations of quantum groupoids, C*-categories, reconstruction theorem
2020 MSC: Primary 18D10, Secondary 16T05, Tertiary 46L05
Theory and Applications of Categories, Vol. 37, 2021, No. 3, pp 57-94.