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MiS Preprint
80/2018

An equivariant pullback structure of trimmable graph C*-algebras

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

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 $\mathcal{O}_2$ and the Toeplitz algebra $\mathcal{T}$. Then we analyze equivariant pullback structures of trimmable graphs yielding the C*-algebras of the Vaksman--Soibelman quantum sphere $S^{2n+1}_q$ and the quantum lens space $L_q^3(l; 1,l)$, respectively.

Received:
Sep 17, 2018
Published:
Sep 20, 2018
MSC Codes:
46L80, 46L85, 58B32

Related publications

inJournal
2022 Journal Open Access
Francesca Arici, Francesco D'Andrea, Piotr M. Hajac and Mariusz Tobolski

An equivariant pullback structure of trimmable graph C*-algebras

In: Journal of noncommutative geometry, 16 (2022) 3, pp. 761-785