Categorical perspectives in noncommutative duality

TL;DR

This paper introduces the categorical framework of noncommutative duality, emphasizing Landstad duality for group actions and coactions, extending classical Pontryagin duality to noncommutative settings.

Contribution

It provides an introduction to the categorical aspects of noncommutative duality, focusing on Landstad duality for actions and coactions of locally compact groups.

Findings

Categorical perspective clarifies noncommutative duality structures

Landstad duality is central to understanding noncommutative duality

Framework generalizes classical Pontryagin duality to noncommutative cases

Abstract

Noncommutative duality for C*-dynamical systems is a vast generalization of Pontryagin duality for locally compact abelian groups. In this series of lectures, we give an introduction to the categorical aspects of this duality, focusing primarily on Landstad duality for actions and coactions of locally compact groups.