Equivariant Dimensions of Graph C*-algebras

Abstract

We explore the recently introduced local-triviality dimensions by studying gauge actions on graph $C^{\ast }$-algebras, as well as the restrictions of the gauge action to finite cyclic subgroups. For $C^{\ast }$-algebras of finite acyclic graphs and finite cycles, we characterize the finiteness of these dimensions, and we further study the gauge actions on many examples of graph $C^{\ast }$-algebras. These include the Toeplitz algebra, Cuntz algebras, and $q$-deformed spheres.

23 pages + references. To appear in Journal of Functional Analysis. Changes from the previous version include removing section 6 on fixed point subalgebras (for length), shortening exposition/proofs, expanding the introduction, and revamping the K-homology arguments in section 5

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Cited by in corpus (2)

• Realizations of free actions via their fixed point algebras
• Leavitt vs. $C^{\ast }$ pullbacks