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1.

図書
図書
1. An introduction to K-theory for C*-algebras (: hbk ; : pbk)
M. Rørdam, F. Larsen, N. Laustsen
出版情報: Cambridge, UK ; New York, NY : Cambridge University Press, 2000  xii, 242 p. ; 24 cm
シリーズ名: London Mathematical Society student texts ; 49
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Preface
C*-Algebra Theory / 1：
C*-algebras and *-homomorphisms / 1.1：
Spectral theory / 1.2：
Matrix algebras / 1.3：
Exercises / 1.4：
Projections and Unitary Elements / 2：
Homotopy classes of unitary elements / 2.1：
Equivalence of projections / 2.2：
Semigroups of projections / 2.3：
The K[subscript 0]-Group of a Unital C*-Algebra / 2.4：
Definition of the K[subscript 0]-group of a unital C*-algebra / 3.1：
Functoriality of K[subscript 0] / 3.2：
Examples / 3.3：
The Functor K[subscript 0] / 3.4：
Definition and functoriality of K[subscript 0] / 4.1：
The standard picture of the group K[subscript 0](A) / 4.2：
Half and split exactness and stability of K[subscript 0] / 4.3：
The Ordered Abelian Group K[subscript 0](A) / 4.4：
The ordered K[subscript 0]-group of stably finite C*-algebras / 5.1：
States on K[subscript 0](A) and traces on A / 5.2：
Inductive Limit C*-Algebras / 5.3：
Products and sums of C*-algebras / 6.1：
Inductive limits / 6.2：
Continuity of K[subscript 0] / 6.3：
Stabilized C*-algebras / 6.4：
Classification of AF-Algebras / 6.5：
Finite dimensional C*-algebras / 7.1：
AF-algebras / 7.2：
Elliott's classification theorem / 7.3：
UHF-algebras / 7.4：
The Functor K[subscript 1] / 7.5：
Definition of the K[subscript 1]-group / 8.1：
Functoriality of K[subscript 1] / 8.2：
K[subscript 1]-groups and determinants / 8.3：
The Index Map / 8.4：
Definition of the index map / 9.1：
The index map and partial isometries / 9.2：
An exact sequence of K-groups / 9.3：
Fredholm operators and Fredholm index / 9.4：
The Higher K-Functors / 9.5：
The isomorphism between K[subscript 1](A) and K[subscript 0](SA) / 10.1：
The long exact sequence in K-theory / 10.2：
Bott Periodicity / 10.3：
The Bott map / 11.1：
The proof of Bott periodicity / 11.2：
Applications of Bott periodicity / 11.3：
Homotopy groups and K-theory / 11.4：
The holomorphic function calculus / 11.5：
The Six-Term Exact Sequence / 11.6：
The exponential map and the six-term exact sequence / 12.1：
An explicit description of the exponential map / 12.2：
Inductive Limits of Dimension Drop Algebras / 12.3：
Dimension drop algebras / 13.1：
Countable Abelian groups as K-groups / 13.2：
References / 13.3：
Table of K-groups
Index of symbols
General index
Preface
C*-Algebra Theory / 1：
C*-algebras and *-homomorphisms / 1.1：
2.

図書
図書
2. An invitation to C[*]-algebras (: us ; : gw)
William Arveson
出版情報: New York : Springer-Verlag, 1976  x, 106 p. ; 24 cm
シリーズ名: Graduate texts in mathematics ; 39
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Fundamentals / 1：
Multiplicity Theorem / 2：
Borel Structures / 3：
From Commutative Algebras to GCR Algebras / 4：
Fundamentals / 1：
Multiplicity Theorem / 2：
Borel Structures / 3：
3.

図書
図書
3. Invitation to C[*]-algebras and topological dynamics
Jun Tomiyama
出版情報: Singapore : World Scientific, c1987  viii, 167 p. ; 23 cm
シリーズ名: World scientific advanced series in dynamical systems ; v. 3
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4.

図書
図書
4. C*-algebra extensions and K-homology (: pbk)
by Ronald G. Douglas
出版情報: Princeton, NJ : Princeton University Press , [Tokyo] : University of Tokyo Press, 1980  vii, 83 p. ; 25 cm
シリーズ名: Annals of mathematics studies ; no. 95
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5.

図書
図書
5. Equivariant K-theory and freeness of group actions on C[*]-algebras (: gw ; : us)
N. Christopher Phillips
出版情報: Berlin ; Tokyo : Springer-Verlag, c1987  viii, 371 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1274
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6.

図書
図書
6. Positive polynomials, convex integral polytopes, and a random walk problem (: gw ; : us)
David E. Handelman
出版情報: Berlin ; Tokyo : Springer-Verlag, c1987  x, 136 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1282
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7.

図書
図書
7. C*-algebras and their automorphism groups
Gert K. Pedersen
出版情報: London ; New York : Academic Press, 1979  ix, 416 p. ; 24 cm
シリーズ名: L.M.S. monographs ; 14
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8.

図書
図書
8. Completely bounded maps and dilations (: us ; : uk)
Vern I. Paulsen
出版情報: Harlow, Essex, England : Longman Scientific & Technical , New York : Wiley, c1986  187 p. ; 25 cm
シリーズ名: Pitman research notes in mathematics series ; 146
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9.

図書
図書
9. C[*]-algebras. Rev. ed
Jacques Dixmier
出版情報: Amsterdam ; New York : North-Holland , New York : sole distributors for the U.S.A. and Canada, Elsevier North Holland, 1982  xiii, 513 p. ; 23 cm
シリーズ名: North-Holland mathematical library ; v. 15
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10.

図書
図書
10. Methods of noncommutative geometry for group C[*]-algebras (: pbk)
Do Ngoc Diep
出版情報: Boca Raton, FL. ; London : Chapman & Hall/CRC, c2000  351 p. ; 24 cm
シリーズ名: Research notes in mathematics ; 416
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Preface
Introduction / 1：
The Scope and an Example / 1.1：
The Problem / 1.1.1：
BDF K-Homology Functor / 1.1.2：
Topological Invariant Index / 1.1.3：
Multidimensional Orbit Methods / 1.2：
Multidimensional Quantization / 1.2.1：
Category O and Globalization of Harish-Chandra Modules / 1.2.2：
KK-theory Invariant Index C* (G) / 1.3：
About KK-Functors / 1.3.1：
Construction and Reduction of the K-theory Invariant Index C* (G) / 1.3.2：
Deformation Quantization and Cyclic Theories / 1.4：
Star-products and Star-representations / 1.4.1：
Periodic Cyclic Homology / 1.4.2：
Chern Characters / 1.4.3：
Bibliographical Remarks / 1.5：
Elementary Theory: An Overview Based on Examples / I：
Classification of MD-Groups / 2：
Definitions / 2.1：
MD-criteria / 2.2：
Classification Theorem / 2.3：
The Structure of C*-algebras of MD-groups / 2.4：
The C*-algebra of Aff R / 3.1：
Statement of Theorems / 3.1.1：
Proof of Theorem 3.1 / 3.1.2：
Proof of Theorem 3.2 / 3.1.3：
Proof of Theorem 3.3 / 3.1.4：
The Structure of C* (Aff C) / 3.2：
Classification of MD[subscript 4]-groups / 3.3：
Real Diamond Group and Semidirect Products R [times] H[subscript 3] / 4.1：
Description of the Coadjoint Orbits / 4.2：
Some Remarks about the Coadjoint Representation / 4.3.1：
Description of Coadjoint Orbits / 4.3.2：
Measurable MD4-foliations / 4.4：
Measurable Foliations after A. Connes / 4.4.1：
Measurable MD[subscript 4]-foliations / 4.4.2：
Topological Classification of MD[subscript 4]-foliations / 4.4.3：
The Structure of C*-algebras of MD[subscript 4]-foliations / 4.5：
C*-algebras of Measurable Foliations / 5.1：
Holonomy Group of Foliations / 5.1.1：
Half-density Bundle / 5.1.2：
Connes-Thom Isomorphism / 5.1.3：
The C*-algebras of Measureable MD[subscript 4]-foliations / 5.2：
C*-algebras of MD[subscript 4]-foliations and Bundle Type / 5.2.1：
C*-algebras of MD[subscript 4]-foliations of Crossed Product Type / 5.2.2：
Advanced Theory: Multidimensional Quantization and the Index of Group C*-algebras / 5.3：
Induced Representations. Mackey Method of Small Subgroups / 6：
Criterion of Inductibility / 6.1.1：
The Mackey Method of Small Subgroups / 6.1.2：
Projective Representations and Mackey Obstructions / 6.1.3：
Symplectic Manifolds with Flat Action of Lie Groups / 6.2：
Flat Action / 6.2.1：
Classification / 6.2.2：
Prequantization / 6.3：
Quantization Procedure / 6.3.1：
Application / 6.3.2：
Polarization / 6.4：
Some Ideas from Physics / 6.4.1：
(F, [sigma])-polarizations and Polarizations / 6.4.2：
Complex Polarizations / 6.4.3：
Weak Lagrangian Distributions / 6.4.4：
Duflo Data / 6.4.5：
Partially Invariant Holomorphically Induced Representations / 6.5：
Holomorphically Induced Representations Lie Derivative / 7.1：
Unitarization / 7.1.1：
Lie Derivation / 7.1.3：
Irreducible Representations of Nilpotent Lie Groups / 7.2：
Duflo Construction / 7.2.1：
Metaplectic Shale-Weil Representation / 7.2.2：
Irreducible Unitary Representations of Nilpotent Lie Groups / 7.2.3：
Irreducible Representations of Extensions of Nilpotent Lie Groups / 7.2.4：
Representations of Connected Reductive Groups / 7.3：
Harish-Chandra Construction of [pi]([Lambda], [lambda]) / 7.3.1：
(Possibly Nonconnected) Reductive Groups / 7.3.2：
The Induction Procedure for General (Separable) Lie Groups / 7.3.3：
Representations of Almost Algebraic Lie Groups / 7.4：
Coisotropic Subalgebras / 7.4.1：
Irreducible Representations / 7.4.2：
The Trace Formula and the Plancherel Formula / 7.5：
Trace Formula / 7.5.1：
Plancherel Formula for Unimodular Groups / 7.5.2：
Reduction, Modification, and Supervision / 7.6：
Reduction to the Semisimple or Reductive Cases / 8.1：
Coisotropic Tangent Distributions / 8.1.1：
([sigma], [chi]F)-polarizations / 8.1.2：
Induced Representations Obtained from the Solvable or Unipotent Polarizations / 8.1.3：
Unitary Representations Arising in the Reduction of the Multidimensional Quantization Procedure / 8.1.4：
Multidimensional Quantization and U(1)-covering / 8.2：
Positive Polarizations / 8.2.1：
Lifted Characters / 8.2.2：
Induced Representations / 8.2.3：
U(1)-covering of Radicals and Semisimple or Reductive Data / 8.2.4：
Induction from Semisimple Data / 8.2.6：
A Reduction of the Multidimensional Quantization Procedure on the U(1)-covering / 8.2.7：
Globalization over U(1)-coverings / 8.3：
Classical Constructions and Three Geometric Complexes / 8.3.1：
Isomorphisms of Cohomologies / 8.3.2：
Maximal Real Polarizations and Change of Polarizations / 8.3.3：
Quantization of Mechanical Systems with Supersymmetry / 8.4：
Hilbert Superbundles with Connection / 8.4.1：
Quantization Superoperators / 8.4.2：
Superpolarizations and Induced Representations / 8.4.3：
Index of Type I C*-algebras / 8.5：
Compact Type Ideals in Type I C*-algebras / 9.1：
Canonical Composition Series / 9.2：
Compactness Criteria for Group C*-algebras / 9.3：
Compactness Criteria / 9.4.1：
Application to Lie Group Representations / 9.5：
The Case of Solvable Lie Groups / 9.5.1：
Generic Representations of Reductive Lie Groups / 9.5.2：
Invariant Index of Group C*-algebras / 9.6：
The Structure of Group C*-algebras / 10.1：
Construction of Index C* (G) / 10.2：
Reduction of the Indices / 10.3：
General Remarks on Computation of Indices / 10.4：
References / 10.5：
Preface
Introduction / 1：
The Scope and an Example / 1.1：
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