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Journal of Operator Theory

Volume 77, Issue 1, Winter 2017  pp. 149-170.

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

Authors:  Takashi Kawahara
Author institution:Department of Mathematics, Kyushu University, Ito, Fukuoka, 819-0395, Japan

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

Keywords: fundamental group, $C^*$-algebra, Picard group, Hilbert module, finite trace

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