Extension of automorphisms to C*-crossed products with non-trivial centre

TL;DR

This paper investigates conditions under which automorphisms of a C*-algebra with a non-trivial center can be extended to its minimal crossed product, using generalized duality theory and group bundle sections.

Contribution

It introduces an obstruction criterion for extending automorphisms to crossed products of C*-algebras with non-trivial centers, based on generalized Doplicher-Roberts duality and Pimsner algebras.

Findings

Identifies an obstruction related to group bundle sections

Provides a criterion for automorphism extension existence

Utilizes generalized duality theory in the analysis

Abstract

Given a quasi-special endomorphism $\rho$ of a C*-algebra A with nontrivial center, we study an extension problem for automorphisms of A to a minimal cross-product B of A by $\rho$. Exploiting some aspects of the underlying generalized Doplicher-Roberts duality theory based on Pimsner algebras, an obstruction to the existence of such extensions is found and described in terms of sections of a suitable group bundle.