Charlesworth, Ian and Nelson, Brent
2025.
On free Stein dimension.
Indiana University Mathematics Journal
|
Preview |
PDF
- Published Version
Download (307kB) | Preview |
Abstract
We establish several properties of the free Stein dimension, an invariant for finitely generated unital tracial *-algebras. We give formulas for its behaviour under direct sums and tensor products with finite dimensional algebras. Among a given set of generators, we show that (approximate) algebraic relations produce (non-approximate) bounds on the free Stein dimension. Particular treatment is given to the case of separable abelian von Neumann algebras, where we show that free Stein dimension is a von Neumann algebra invariant. In addition, we show that under mild assumptions L2-rigidity implies a free Stein dimension of one. Finally, we use limits superior/inferior to extend the free Stein dimension to a von Neumann algebra invariant—which is substantially more difficult to compute in general—and compute it in several cases of interest.
| Item Type: | Article |
|---|---|
| Date Type: | Published Online |
| Status: | In Press |
| Schools: | Schools > Mathematics |
| Publisher: | Indiana University Mathematics Journal |
| ISSN: | 0022-2518 |
| Date of First Compliant Deposit: | 17 January 2024 |
| Date of Acceptance: | 6 January 2024 |
| Last Modified: | 04 Jun 2025 11:45 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/165568 |
Actions (repository staff only)
 |
Edit Item |
Download Statistics
Download Statistics