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

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Leonid Vainerman and Jean-Michel Vallin

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.

Published 2021-02-02.

http://www.tac.mta.ca/tac/volumes/37/3/37-03.pdf

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