Inductive limits of partial crossed products
Abstract
Let $$\big ((A^{(i)}, G, \alpha ^{(i)}), \phi _i\big )_{i \in \mathbb {N}}$$ be an inductive sequence of partial dynamical systems. We prove the existence of an induced partial action $$\alpha $$ of $$G$$ on the inductive limit $$A=\varinjlim A^{(i)}$$ . We call $$\alpha $$ the inductive limit partial action. Furthermore, we show the corresponding partial crossed product $$A\rtimes _{\alpha }G$$ is canonically isomorphic to $$\varinjlim A^{(i)}\rtimes _{\alpha ^{(i)}}G$$ . We also study the globalization of the inductive limit partial action $$\alpha $$ , its finite Rokhlin dimension and tracial states on $$A\rtimes _{\alpha }G$$ .
Fields of Study & Subjects
Advanced Operator Algebra Research
Geometry and complex manifolds
Holomorphic and Operator Theory
Publication details
- Journal / source
- Semigroup Forum
- Publisher
- Springer Science and Business Media LLC
- Volume
- 112
- Issue
- 1
- Pages
- 155–167
- Publication date
- 5 January 2026
- Language
- EN