Geometry of the sphere of a Hilbert module

The sphere SX = {x ∈ X:〈x, x〉 = 1} of a right Hilbert C*-module X over a unital C*-algebra B is studied using differential geometric techniques. An action of the unitary group of the algebra ℒ B(X) of adjointable B-module operators of X makes SX a homogeneous space of this group. A reductive structu...

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Autores principales: Andrughow, E., Corach, G., Stojanoff, D.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03050041_v127_n2_p295_Andrughow
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_03050041_v127_n2_p295_Andrughow
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spelling todo:paper_03050041_v127_n2_p295_Andrughow2023-10-03T15:21:09Z Geometry of the sphere of a Hilbert module Andrughow, E. Corach, G. Stojanoff, D. The sphere SX = {x ∈ X:〈x, x〉 = 1} of a right Hilbert C*-module X over a unital C*-algebra B is studied using differential geometric techniques. An action of the unitary group of the algebra ℒ B(X) of adjointable B-module operators of X makes SX a homogeneous space of this group. A reductive structure is introduced, as well as a Finsler metric. Metric properties of the geodesic curves are established. In the case B a von Neumann algebra and X self-dual, the fundamental group of SX is computed. © 1999 Cambridge Philosophical Society. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03050041_v127_n2_p295_Andrughow
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description The sphere SX = {x ∈ X:〈x, x〉 = 1} of a right Hilbert C*-module X over a unital C*-algebra B is studied using differential geometric techniques. An action of the unitary group of the algebra ℒ B(X) of adjointable B-module operators of X makes SX a homogeneous space of this group. A reductive structure is introduced, as well as a Finsler metric. Metric properties of the geodesic curves are established. In the case B a von Neumann algebra and X self-dual, the fundamental group of SX is computed. © 1999 Cambridge Philosophical Society.
format JOUR
author Andrughow, E.
Corach, G.
Stojanoff, D.
spellingShingle Andrughow, E.
Corach, G.
Stojanoff, D.
Geometry of the sphere of a Hilbert module
author_facet Andrughow, E.
Corach, G.
Stojanoff, D.
author_sort Andrughow, E.
title Geometry of the sphere of a Hilbert module
title_short Geometry of the sphere of a Hilbert module
title_full Geometry of the sphere of a Hilbert module
title_fullStr Geometry of the sphere of a Hilbert module
title_full_unstemmed Geometry of the sphere of a Hilbert module
title_sort geometry of the sphere of a hilbert module
url http://hdl.handle.net/20.500.12110/paper_03050041_v127_n2_p295_Andrughow
work_keys_str_mv AT andrughowe geometryofthesphereofahilbertmodule
AT corachg geometryofthesphereofahilbertmodule
AT stojanoffd geometryofthesphereofahilbertmodule
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