Generic dynamics and monotone complete \(C^*\)-algebras. (Q2760146)

A (unital) \(C^ *\)-algebra \(A\) is monotone complete if each upward directed upper bounded subset of the self-adjoint part \(A_ h\) of \(A\) has a least upper bound in \(A_ h\).NEWLINENEWLINEThe author gives a sketch of some main aspects of monotone complete \(C^ *\)-algebras and the generic dynamics factor which is a monotone complete \(AW ^ *\)-factor. Furthermore, some information on the outer automorphism group of the generic dynamics factor is discussed. In particular, it is indicated that this group contains every countable group and is therefore large [ see \textit{K. Saitô} and \textit{J. D. Maitland Wright}, J. Math. Anal. Appl. 248, 41--68 (2000; Zbl 1032.46532)]. Note that the outer automorphism group of a \(C^ *\)-algebra may be very small, e.g., the outer automorphism group of \(B(H)\) is \(0\).NEWLINENEWLINEFor the entire collection see [Zbl 0971.00063].