Fischer's approach to deformation of coactions

TL;DR

This paper introduces a new framework for deforming $C^*$-algebras using coactions of locally compact groups, extending existing theories and demonstrating the equivalence of different deformation methods.

Contribution

It provides a rigorous framework for deformation via coactions, extending Fischer's approach and comparing various procedures using Landstad duality.

Findings

Demonstrates the equivalence of different deformation procedures

Extends Fischer's construction to maximal coactions

Provides a unified perspective on operator algebra deformations

Abstract

This paper explores a novel approach to the deformation of $C^*$-algebras via coactions of locally compact groups, emphasizing Fischer's construction in the context of maximal coactions. We establish a rigorous framework for understanding how deformations arise from group coactions, extending previous work by Bhowmick, Neshveyev, and Sangha. Using Landstad duality, we compare different deformation procedures, demonstrating their equivalence and efficiency in constructing twisted versions of given $C^*$-algebras. Our results provide deeper insights into the interplay between exotic crossed products, coaction duality, and operator algebra deformations, offering a unified perspective for further generalizations.