arXiv subjects
Publications and source records attributed to Takashi Kawahara.
We consider the realization of fundamental groups of $AF$-algebras in a certain class. We find the fundametal groups of $AF$-algebras with finite dimensional trace space which is not realizable as a fundamental group of von Neumann algebras.
We introduce the fundamental group $F(\mathcal{M})$ of a finite von Neumann algebra $\mathcal{M}$ with finite dimensional normal trace space. The form of $F(\mathcal{M})$ is completely determined. Moreover, there exists a finite von Neumann algebra $\mathcal{M}$ with finite dimensional normal trace space such that $F(\mathcal{M})=G$ for any conceivable groups $G$ as fundamental group.
We introduce the fundamental group $rF(cA)$ 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 $rF(cA)=\set{I_{n}}$. Our study is due to the results of fundamental group by Nawata and Watatani.