A note on trace scaling actions and fundamental groups of $C^*$-algebras

Norio Nawata

A note on trace scaling actions and fundamental groups of $C^*$-algebras

Operator Algebras 2011-09-09 v3

Authors: Norio Nawata

Abstract

Using Effros-Handelman-Shen theorem and Elliott's classification theorem of AF algebras, we show that there exists a unital simple AF algebra A with unique trace such that $A\otimes \mathbb{K}$ admits no trace scaling action of the fundamental group of A.

Keywords

trace scaling action fundamental group AF algebra unique trace Elliott classification Effros-Handelman-Shen theorem

Cite

@article{arxiv.1009.1722,
  title  = {A note on trace scaling actions and fundamental groups of $C^*$-algebras},
  author = {Norio Nawata},
  journal= {arXiv preprint arXiv:1009.1722},
  year   = {2011}
}

Comments

6 pages, Some typos are corrected

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