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
MSC-Numbers: 46L80, 46L85, 58B32
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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 Sq2n+1 and the quantum lens space Lq3(l;1,l), respectively.