Torsion theories for finite von Neumann algebras
| dc.creator | Vas, Lia | |
| dc.date | 2007-02-18 | |
| dc.date.accessioned | 2026-07-07T07:47:34Z | |
| dc.date.available | 2026-07-07T07:47:34Z | |
| dc.description | The study of modules over a finite von Neumann algebra ${\mathcal A}$ can be advanced by the use of torsion theories. In this work, some torsion theories for ${\mathcal A}$ are presented, compared and studied. In particular, we prove that the torsion theory $(\mathrm{\bf T},\mathrm{\bf P})$ (in which a module is torsion if it is zero-dimensional) is equal to both Lambek and Goldie torsion theories for ${\mathcal A}$. Using torsion theories, we describe the injective envelope of a finitely generated projective ${\mathcal A}$-module and the inverse of the isomorphism $K_0({\mathcal A})\to K_0({\mathcal U}),$ where ${\mathcal U}$ is the algebra of affiliated operators of ${\mathcal A}.$ Then, the formula for computing the capacity of a finitely generated module is obtained. Lastly, we study the behavior of the torsion and torsion-free classes when passing from a subalgebra ${\mathcal B}$ of a finite von Neumann algebra ${\mathcal A}$ to ${\mathcal A}$. With these results, we prove that the capacity is invariant under the induction of a ${\mathcal B}$-module. | |
| dc.identifier | https://arxiv.org/abs/math/0702527 | |
| dc.identifier | http://arxiv.org/abs/math/0702527 | |
| dc.identifier | L. Vas, Torsion Theories for Finite von Neumann Algebras, Communications in Algebra 33 (2005), no. 3, 663 - 688 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124210 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Operator Algebras | |
| dc.subject | 16W99, 46L99, 16S90, 19K99 | |
| dc.title | Torsion theories for finite von Neumann algebras | |
| dc.type | text |