Admissibility of C*-covers for operator algebra dynamical systems
Abstract
We characterize when a C∗-cover admits a C∗-dynamical extension of dynamics on an operator algebra in terms of the boundary ideal structure for the operator algebra in its maximal representation and show that the C∗-covers that admit such an extension form a complete lattice. We study dynamical systems arising from groups acting via inner automorphisms in a C∗-cover and produce an example of a C∗-cover that admits no extension of dynamics on a finite-dimensional non-self-adjoint operator algebra. We construct a partial action on a class of C∗-covers that recovers the crossed product of an operator algebra as a subalgebra of the partial crossed product, even when the C∗-cover admits no dynamical extension.
Fields of Study & Subjects
Advanced Operator Algebra Research
Holomorphic and Operator Theory
Advanced Banach Space Theory
Publication details
- Journal / source
- Journal of Operator Theory
- Volume
- 95
- Issue
- 1
- Pages
- 223–245
- Publication date
- 1 March 2026
- Language
- EN