A class of AF-algebras up to universal UHF-algebra stability

Saeed Ghasemi

A class of AF-algebras up to universal UHF-algebra stability

Operator Algebras 2020-09-11 v1

Authors: Saeed Ghasemi

Abstract

We will show that separable unital AF-algebras whose Bratteli diagrams do not allow converging two nodes into one node, can be classified up to the tensor product with the universal UHF-algebra $\Q$ only by their trace spaces. That is, if $\A$ and $\B$ are such AF-algebras, then $T(A)=T(B)$ if and only if $\A\otimes \Q \cong \B\otimes \Q$ .

Keywords

AF-algebras UHF-algebra Bratteli diagrams trace spaces classification tensor product

Cite

@article{arxiv.2009.04664,
  title  = {A class of AF-algebras up to universal UHF-algebra stability},
  author = {Saeed Ghasemi},
  journal= {arXiv preprint arXiv:2009.04664},
  year   = {2020}
}

Comments

8 pages

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