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

DOI10.7900/JOT.2016MAR08.2099zbMATH Open1399.46091arXiv1508.07605OpenAlexW2964025843MaRDI QIDQ4978086

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Publication date: 17 August 2017

Published in: (Search for Journal in Brave)

Abstract: We introduce the fundamental group $F(cA)$ of a unital $C^{*}$-algebra $cA$ 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 $F(cA)=set{I}_n$. Our study is due to the results of fundamental group by Nawata and Watatani.

Full work available at URL: https://arxiv.org/abs/1508.07605

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