Approximately finite-dimensional 𝐶*-algebras and Bratteli diagrams

Lazar, A. J.; Taylor, D. C.

doi:10.1090/S0002-9947-1980-0567100-9

Approximately finite-dimensional $C^{\ast }$-algebras and Bratteli diagrams
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by A. J. Lazar and D. C. Taylor

Trans. Amer. Math. Soc. 259 (1980), 599-619

DOI: https://doi.org/10.1090/S0002-9947-1980-0567100-9

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Abstract:

We determine properties of an AF algebra by observing the characteristics of its diagram. In particular, we characterize AF algebras that are liminal, postliminal, antiliminal and with continuous trace; moreover, we characterize liminal AF algebras with Hausdorff spectrum. Some elementary examples of AF algebras with certain desired properties are constructed by using these characterizations.

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algebras

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Type

algebras

73

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