Fundamental group of $C^{*}$-algebras with finite dimensional trace space

Takashi Kawahara

Fundamental group of $C^{*}$-algebras with finite dimensional trace space

Operator Algebras 2016-02-11 v2

Authors: Takashi Kawahara

Abstract

We introduce the fundamental group $\r{F}(\c{A})$ of a unital $C^*$ -algebra $\c{A}$ with finite dimensional trace space. The elements of fundamental group are restricted by K-theoretical obstruction and positivity. Moreover we show there are uncountably many mutually nonisomorphic simple $C^{*}$ -algebras such that $\r{F}(\c{A})=\set{I_{n}}$ . Our study is due to the results of fundamental group by Nawata and Watatani.

Keywords

fundamental group C*-algebras finite dimensional trace space K-theoretical obstruction simple C*-algebras

Cite

@article{arxiv.1508.07605,
  title  = {Fundamental group of $C^{*}$-algebras with finite dimensional trace space},
  author = {Takashi Kawahara},
  journal= {arXiv preprint arXiv:1508.07605},
  year   = {2016}
}

Comments

arXiv admin note: text overlap with arXiv:0904.1081 by other authors

Fundamental group of $C^{*}$-algebras with finite dimensional trace space

Abstract

Keywords

Cite

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