Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
0. Introduction........................................................................................................................................................................5
I. C*-semigroup bundles and C*-algebras whose irreducible representations are all finite dimensional.................................7
1. C*-semigroup bundles and their morphisms......................................................................................................................7
2. The universal C*-semigroup bundle of a C*-algebra........................................................................................................10
3. Abelian and associative C*-semigroup bundles and the extension of compatible sections..............................................13
4. Existence and "uniqueness" of representation semigroups and C*-semigroup bundles..................................................23
5. Duality between certain C*-semigroup bundles and certain C*-algebras.........................................................................29
6. The core of a representation semigroup..........................................................................................................................35
II. The calculation of $ΠH¹_R$ for certain C*-bundles..........................................................................................................39
1. The functor $ΠH¹_R$.......................................................................................................................................................39
2. C*-bundle embeddings, multiplicity bundles and $MH¹_R$..............................................................................................44
3. Finite order C*-bundles....................................................................................................................................................52
4. Third order C*-bundles with finite dimensional fibres over cones over pairs of compact Riemannian manifolds..............58
5. A remark on the continuity of the map $f: X → S_A$ of I.5.3.3.........................................................................................66
III. Applications and open problems......................................................................................................................................67
1. Applications and final remarks.........................................................................................................................................67
2. Applications.....................................................................................................................................................................76
3. Open problems and final remarks....................................................................................................................................81
Appendix. A simple proof of Dupre's classification Theorem II.1.1 for a restricted class of bundles.....................................82
References..........................................................................................................................................................................87
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
290
Liczba stron
87
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCXC
Daty
wydano
1989
Twórcy
autor
Bibliografia
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- [Di; 69] J. Dixmier, Les C*-algèbres et leurs représentations, Gauthier-Villars, Paris 1969.
- [Do; 63] A. Dold, Partitions of unity in the theory of fibrations, Ann. Math. 79 (1963), 223-255.
- [Du; 1] M. J. Dupré, Cohomology for classifying categories of Banach bundles, summary, preprint, Tulane University.
- [Du; 79] M. J. Dupré, Classification and structure of C*-algebra bundles, Mem. Amer. Math. Soc. 222 (1979).
- [Du; 2] M. J. Dupré, The classification and structure of C*-algebra bundles, II, summary, preprint, Tulane University.
- [Du; 3] M. J. Dupré, Duality for C*-algebras, preprint, Tulane University.
- [DG; 83] M. J. Dupré and R. M. Gillette, Banach Bundles, Banach Modules and Automorphisms of C*-Algebras, Research Notes Math., Pitman, London 1983.
- [Ev; 79] B. D. Evans, The C*-algebras of compact transformation groups, Ph. D. dissertation. University of Pennsylvania, 1979.
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- [Ro; 76] J. Rosenberg, The C*-algebras of some real and p-adic solvable groups. Pacific J. Math. 65 (1976), 175-192.
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- [St; 51] N. Steenrod, The Topology of Fibre Bundles, Princeton University Press, 1951.
- [Ta; 67] M. Takesaki, A duality in the representation theory of C*-algebras, Ann. of Math. 85, 2nd series (1967).
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- [Ve; 84] A. Verona. Stratified Mappings - Structure and Triangulability, Springer-Verlag. Berlin Heidelberg 1984.
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