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The Category of Bratteli Diagrams

  • Massoud Amini (a1), George A. Elliott (a2) and Nasser Golestani (a1)

Abstract

A category structure for Bratteli diagrams is proposed and a functor from the category of $\text{AF}$ algebras to the category of Bratteli diagrams is constructed. Since isomorphism of Bratteli diagrams in this category coincides with Bratteli’s notion of equivalence, we obtain in particular a functorial formulation of Bratteli’s classification of $\text{AF}$ algebras (and at the same time, of Glimm’s classification of $\text{UHF}$ algebras). It is shown that the three approaches to classification of $\text{AF}$ algebras, namely, through Bratteli diagrams, $\text{K}$ -theory, and a certain natural abstract classifying category, are essentially the same from a categorical point of view.

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Keywords

The Category of Bratteli Diagrams

  • Massoud Amini (a1), George A. Elliott (a2) and Nasser Golestani (a1)

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