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

Leonid Vainerman (1) , Jean-Michel Vallin (2, 3)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 IDP - Institut Denis Poisson
3 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

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.

Mots clés: Coactions and corepresentations of quantum groupoids; C* -categories; reconstruction theorem

Domaines: Algèbres quantiques [math.QA]; Algèbres d'opérateurs [math.OA]

Leonid Vainerman, Jean-Michel Vallin. Yetter-Drinfel'd algebras and coideals of Weak Hopf C * -Algebras. 2020. ⟨hal-02886793v1⟩