Yetter-Drinfel'd algebras and coideals of Weak Hopf $C^{\ast }$-Algebras

Abstract

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

References in corpus (6)

• Lectures on tensor categories
• Tannaka-Krein reconstruction and a characterization of modular tensor categories
• Finitely semisimple spherical categories and modular categories are self-dual
• Deformation of finite dimensional C*-quantum groupoids
• Reconstruction of weak bialgebra maps and its applications
• Tannaka-Krein reconstruction for coactions of finite quantum groupoids