Coactions on C*-algebras and universal properties

TL;DR

This paper explores the universal properties of maximalization and normalization of coactions on C*-algebras using categorical frameworks, providing new proofs for these fundamental concepts.

Contribution

It introduces a categorical approach to derive the universal properties of maximalization and normalization of coactions, offering dual proofs and deeper theoretical insight.

Findings

Categorical framework effectively explains maximalization universal property

Dual proof provided for normalization universal property

Enhances understanding of coaction structures in C*-algebras

Abstract

It is well-known that the maximalization of a coaction of a locally compact group on a C*-algebra enjoys a universal property. We show how this important property can be deduced from a categorical framework by exploiting certain properties of the maximalization functor for coactions. We also provide a dual proof for the universal property of normalization of coactions.