Defines ring structures on K_*(A) for AF cores A of graph C*-algebras via embeddings and shows generation by noncommutative line bundles under graph conditions, with examples including quantum projective spaces.
Pullbacks of graph C*-algebras from admissible pushouts of graphs
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abstract
We define an admissible decomposition of a graph $E$ into subgraphs $F_1$ and $F_2$, and consider the intersection graph $F_1\cap F_2$ as a subgraph of both $F_1$ and $F_2$. We prove that, if the graph $E$ is row finite and its decomposition into the subgraphs $F_1$ and $F_2$ is admissible, then the graph C*-algebra $C^*(E)$ of $E$ is the pullback C*-algebra of the canonical surjections from $C^*(F_1)$ and $C^*(F_2)$ onto $C^*(F_1\cap F_2)$.
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math.KT 1years
2024 1verdicts
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On the K-theory of the AF core of a graph C*-algebra
Defines ring structures on K_*(A) for AF cores A of graph C*-algebras via embeddings and shows generation by noncommutative line bundles under graph conditions, with examples including quantum projective spaces.