Extension of automorphisms to C*-crossed products with non-trivial centre
Roberto Conti, Ezio Vasselli

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 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 . 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.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Holomorphic and Operator Theory
