The category of Bratteli diagrams
Operator Algebras
2019-08-15 v1
Abstract
A category structure for Bratteli diagrams is proposed and a functor from the category of 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 AF algebras (and at the same time, of Glimm's classification of UHF algebras). It is shown that the three approaches to classification of AF algebras, namely, through Bratteli diagrams, K-theory, and abstract classifying categories, are essentially the same from a categorical point of view.
Cite
@article{arxiv.1407.8413,
title = {The category of Bratteli diagrams},
author = {Massoud Amini and George A. Elliott and Nasser Golestani},
journal= {arXiv preprint arXiv:1407.8413},
year = {2019}
}
Comments
36 pages