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Geometry of the sphere of a Hilbert module

Published online by Cambridge University Press:  01 September 1999

ESTEBAN ANDRUCHOW ,
GUSTAVO CORACH  and
DEMETRIO STOJANOFF
ESTEBAN ANDRUCHOW
Affiliation:
Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.A. Roca 850, 1663 San Miguel, Argentina
GUSTAVO CORACH
Affiliation:
Instituto Argentino de Matemática, Saavedra 15, 1083 Buenos Aires, Argentina Departamento de Matemática, FCEN, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
DEMETRIO STOJANOFF
Affiliation:
Instituto Argentino de Matemática, Saavedra 15, 1083 Buenos Aires, Argentina Departamento de Matemática, FCEN, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
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Abstract

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 [Lscr ]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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 127 , Issue 2 , September 1999 , pp. 295 - 315
Copyright
The Cambridge Philosophical Society 1999

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