Geodesics of projections in von Neumann algebras
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
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American Mathematical Society
2024
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| Acceso en línea: | http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1801 |
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I71-R177-UNGS-18012024-12-23T13:21:45Z Geodesics of projections in von Neumann algebras Andruchow, Esteban Projections Geodesics of projections Von Neumann algebras Index for subfactors Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina. Let A be a von Neumann algebra and PA the manifold of projections in A. There is a natural linear connection in PA, which in the finite dimensional case coincides with the the Levi-Civita connection of the Grassmann manifold of Cn. In this paper we show that two projections p, q can be joined by a geodesic, which has minimal length (with respect to the metric given by the usual norm of A), if and only if p ? q? ? p? ? q, where ? stands for the Murray-von Neumann equivalence of projections. It is shown that the minimal geodesic is unique if and only if p ? q? = p? ? q = 0. If A is a finite factor, any pair of projections in the same connected component of PA (i.e., with the same trace) can be joined by a minimal geodesic. We explore certain relations with Jones’ index theory for subfactors. For instance, it is shown that if N ?M are II1 factors with finite index [M : N ] = t?1, then the geodesic distance d(eN , eM) between the induced projections eN and eM is d(eN , eM) = arccos(t1/2). 2024-12-23T13:21:44Z 2024-12-23T13:21:44Z 2021 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion Andruchow, E. (7-2021). Geodesics of projections in von Neumann algebras. Proceedings of the American Mathematical Society, 149(10), 4501-4513. 0002-9939 http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1801 eng http://dx.doi.org/10.1090/proc/15568 info:eu-repo/semantics/restrictedAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf American Mathematical Society Proceedings of the American Mathematical Society. (Jul. 2021); 149(10): 4501-4513 https://www.ams.org/proc/2021-149-10/S0002-9939-2021-15568-8/ |
| institution |
Universidad Nacional de General Sarmiento |
| institution_str |
I-71 |
| repository_str |
R-177 |
| collection |
Repositorio Institucional Digital de Acceso Abierto (UNGS) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| topic |
Projections Geodesics of projections Von Neumann algebras Index for subfactors |
| spellingShingle |
Projections Geodesics of projections Von Neumann algebras Index for subfactors Andruchow, Esteban Geodesics of projections in von Neumann algebras |
| topic_facet |
Projections Geodesics of projections Von Neumann algebras Index for subfactors |
| description |
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. |
| format |
Artículo Artículo publishedVersion |
| author |
Andruchow, Esteban |
| author_facet |
Andruchow, Esteban |
| author_sort |
Andruchow, Esteban |
| title |
Geodesics of projections in von Neumann algebras |
| title_short |
Geodesics of projections in von Neumann algebras |
| title_full |
Geodesics of projections in von Neumann algebras |
| title_fullStr |
Geodesics of projections in von Neumann algebras |
| title_full_unstemmed |
Geodesics of projections in von Neumann algebras |
| title_sort |
geodesics of projections in von neumann algebras |
| publisher |
American Mathematical Society |
| publishDate |
2024 |
| url |
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1801 |
| work_keys_str_mv |
AT andruchowesteban geodesicsofprojectionsinvonneumannalgebras |
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1824528619475566592 |