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.
DOI: http://dx.doi.org/10.7900/jot.2016mar08.2099
Keywords: fundamental group, $C^*$-algebra, Picard group, Hilbert module, finite trace
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