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C-semigroup bundles and C-algebras whose irreducible representations are all finite dimensional

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Müller T.

Instytut Matematyczny Polskiej Akademii Nauk

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

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1 Müller T.

1 1989

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C-semigroup bundles and C-algebras whose irreducible representations are all finite dimensional