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Goodearl, ‘Leavitt path algebras and direct limits’, Rings, modules and representations, Contemporary Mathematics
- Publisher
- Wiley
- Copyright
- © 2021 London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/blms.12389
- Publisher site
- See Article on Publisher Site
Abstract
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 a recipe for determining the quantum space obtained by shrinking a quantum subspace. There are numerous examples from noncommutative topology, such as quantum complex projective spaces (including the standard Podleś quantum sphere) and quantum teardrops, that instantiate the result. Furthermore, to go beyond AF graph C*‐algebras, we consider extensions of graphs over sinks and prove an analogous theorem for the thus obtained graph C*‐algebras.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Feb 1, 2021