Uniform property $\Gamma$ and finite dimensional tracial boundaries

Samuel Evington; Christopher Schafhauser

Uniform property $\Gamma$ and finite dimensional tracial boundaries

Operator Algebras 2024-11-27 v2

Authors: Samuel Evington , Christopher Schafhauser

Abstract

We prove that a C $^*$ -algebra $A$ has uniform property $\Gamma$ if the set of extremal tracial states, $\partial_e T(A)$ , is a non-empty compact space of finite covering dimension and for each $\tau \in \partial_e T(A)$ , the von Neumann algebra $\pi_\tau(A)''$ arising from the GNS representation has property $\Gamma$ .

Keywords

C*-algebra property Gamma tracial state GNS representation finite covering dimension

Cite

@article{arxiv.2407.16612,
  title  = {Uniform property $\Gamma$ and finite dimensional tracial boundaries},
  author = {Samuel Evington and Christopher Schafhauser},
  journal= {arXiv preprint arXiv:2407.16612},
  year   = {2024}
}

Comments

24 pages; accepted version; Canad J. Math., to appear

Uniform property $\Gamma$ and finite dimensional tracial boundaries

Abstract

Keywords

Cite

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