• Corpus ID: 119120328

An equivariant pullback structure of trimmable graph C*-algebras

  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},
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… 

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