Fischer's approach to deformation of coactions

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.