On generalization of the Cuntz algebras (Q2711739)

The authors study a \(C^*\)-algebra \({\mathcal O}_{n,\{ \alpha_k\}_{k=1}^n}\) generated by isometries \(s_1,\ldots ,s_n\) such that NEWLINE\[NEWLINE\sum_{k=1}^n\alpha_ks_ks_k^*=I,NEWLINE\]NEWLINE where \(0<\alpha_k<1\). It is shown that the algebra is \(*\)-wild if \(n=4\), \(\alpha_1=\ldots =\alpha_4=1/2\). A criterion of \(*\)-wildness for the case \(n=3\) is established.NEWLINENEWLINEFor the entire collection see [Zbl 0937.00046].