An equivariant pullback structure of trimmable graph C*-algebras

Francesca Arici, Francesco D'Andrea, Piotr M. Hajac, and Mariusz Tobolski

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Submission date: 17. Sep. 2018
Pages: 26
Bibtex
MSC-Numbers: 46L80, 46L85, 58B32
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Abstract:
We prove that the graph C*-algebra C^∗(E) of a trimmable graph E is U(1)-equivariantly isomorphic to a pullback C*-algebra of a subgraph C*-algebra C^∗(E′′) and the C*-algebra of functions on a circle tensored with another subgraph C*-algebra C^∗(E′). This allows us to unravel the structure and K-theory of the fixed-point subalgebra C^∗(E)^U(1) through the (typically simpler) C*-algebras C^∗(E′), C^∗(E′′) and C^∗(E′′)^U(1). As examples of trimmable graphs, we consider one-loop extensions of the standard graphs encoding respectively the Cuntz algebra 𝒪₂ and the Toeplitz algebra 𝒯 . Then we analyze equivariant pullback structures of trimmable graphs yielding the C*-algebras of the Vaksman–Soibelman quantum sphere S_q²ⁿ⁺¹ and the quantum lens space L_q³(l;1,l), respectively.