$C^*$-pseudo-Kac systems and duality for coactions of concrete Hopf $C^*$-bimodules

TL;DR

This paper develops a duality theory for coactions of concrete Hopf C*-bimodules within the framework of weak C*-pseudo-Kac systems, introducing reduced crossed products and establishing an analogue of Baaj-Skandalis duality.

Contribution

It introduces a new duality framework for coactions of concrete Hopf C*-bimodules using weak C*-pseudo-Kac systems, including the construction of reduced crossed products.

Findings

Established an analogue of Baaj-Skandalis duality for these coactions.

Defined reduced crossed products and dual coactions in this setting.

Extended duality theory to the framework of weak C*-pseudo-Kac systems.

Abstract

We study coactions of concrete Hopf $C^{*}$-bimodules in the framework of (weak) $C^{*}$-pseudo-Kac systems, define reduced crossed products and dual coactions, and prove an analogue of Baaj-Skandalis duality.