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

Abstract

We introduce the fundamental group $rF(cA)$ of a unital $C^{\ast }$-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 $C^{\ast }$-algebras such that $rF(cA)=\{I_n\}$. Our study is due to the results of fundamental group by Nawata and Watatani.

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