# An equivariant pullback structure of trimmable graph C*-algebras

@article{Arici2018AnEP, title={An equivariant pullback structure of trimmable graph C*-algebras}, author={Francesca Arici and Francesco D’Andrea and Piotr M. Hajac and Mariusz Tobolski}, journal={arXiv: K-Theory and Homology}, year={2018} }

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…

## 8 Citations

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We find a substantial class of pairs of ∗ ‐homomorphisms between graph C*‐algebras of the form C∗(E)↪C∗(G)↞C∗(F) whose pullback C*‐algebra is an AF graph C*‐algebra. Our result can be interpreted as…

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- MathematicsBanach Center Publications
- 2020

By a diagonal embedding of $U(1)$ in $SU_q(m)$, we prolongate the diagonal circle action on the Vaksman-Soibelman quantum sphere $S^{2n+1}_q$ to the $SU_q(m)$-action on the prolongated bundle. Then…

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The multipullback quantization of complex projective spaces lacks the naive quantum CW-complex structure because the quantization of an embedding of the nskeleton into the (n + 1)-skeleton does not…

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Motivated by recent results in graph C*-algebras concerning an equivariant pushout structure of the Vaksman-Soibelman quantum odd spheres, we introduce a class of graphs called trimmable. Then we…

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