On outer automorphisms of certain graph $C^{*}$-algebras
Swarnendu Datta, Debashish Goswami, Soumalya Joardar

TL;DR
This paper constructs specific directed graphs whose associated C*-algebras have K_0 groups isomorphic to any given countable abelian group, and shows how automorphisms of the group lift to automorphisms of the algebra.
Contribution
It provides a method to realize any countable abelian group as the K_0 group of a graph C*-algebra and demonstrates how automorphisms of the group correspond to automorphisms of the algebra.
Findings
Constructed graphs with prescribed K_0 groups
Automorphisms of the abelian group lift to algebra automorphisms
Established a canonical isomorphism between K_0 and the given group
Abstract
Given a countable abelian group , we construct a row finite directed graph such that the -group of the graph -algebra is canonically isomorphic to . Moreover, each element of is a lift of an automorphism of the graph -algebra .
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Taxonomy
TopicsAdvanced Operator Algebra Research · Holomorphic and Operator Theory · Advanced Banach Space Theory
