English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this article, we generalize to the case of regular locally compact quantumgroups, two important results concerning actions of compact quantum groups. Let$G_1$ and $G_2$ be two monoidally equivalent regular locally compact quantumgroups in the sense of De Commer. We introduce an induction procedure and webuild an equivalence of the categories ${A}^{G_1}$ and ${A}^{G_2}$ consistingof continuous actions of $G_1$ and $G_2$ on $C^*$-algebras. As an applicationof this result, we derive a canonical equivalence of the categories${KK}^{G_1}$ and ${KK}^{G_2}$. We introduce and investigate a notion of actionson $C^*$-algebras of measured quantum groupoids on a finite basis. The proof ofthe equivalence between ${KK}^{G_1}$ and ${KK}^{G_2}$ relies on a version ofthe Takesaki-Takai duality theorem for continuous actions on $C^*$-algebras ofmeasured quantum groupoids on a finite basis.

\'Equivalence mono\"idale de groupes quantiques et K-th\'eorie bivariante