1. Coactions of compact groups on $M_n$
- Author
-
Kaliszewski, S., Landstad, Magnus B., and Quigg, John
- Subjects
Mathematics - Operator Algebras ,46L05, 46L55 - Abstract
We prove that every coaction of a compact group on a finite-dimensional $C^*$-algebra is associated with a Fell bundle. Every coaction of a compact group on a matrix algebra is implemented by a unitary operator. A coaction of a compact group on $M_n$ is inner if and only if its fixed-point algebra has an abelian $C^*$-subalgebra of dimension $n$. Investigating the existence of effective ergodic coactions on $M_n$ reveals that $\operatorname{SO}(3)$ has them, while $\operatorname{SU}(2)$ does not. We give explicit examples of the two smallest finite nonabelian groups having effective ergodic coactions on $M_n$., Comment: 20 pages
- Published
- 2024