Blackadar B. — K-theory for operator algebras :: Электронная библиотека попечительского совета мехмата МГУ

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Blackadar B. — K-theory for operator algebras

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Название: K-theory for operator algebras

Автор: Blackadar B.

Аннотация:

K-theory has helped convert the theory of operator algebras from a simple branch of functional analysis to a subject with broad applicability throughout mathematics, especially in geometry and topology, and many mathematicians of diverse backgrounds must learn the essential parts of the theory. This book is the only comprehensive treatment of K-theory for operator algebras, and is intended to help students, non specialists, and specialists learn the subject. This first paperback printing has been revised and expanded and contains an updated reference list. This book develops K-theory, the theory of extensions, and Kasparov's bivariant KK-theory for C*-algebras. Special topics covered include the theory of AF algebras, axiomatic K-theory, the Universal Coefficient Theorem, and E-theory. Although the book is technically complete, motivation and intuition are emphasized. Many examples and applications are discussed.

Язык:

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 1998

Количество страниц: 300

Добавлена в каталог: 24.11.2004

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Предметный указатель

"Compact perturbation"      17.2.4
"Real" C*-algebra      19.9.7
-index theorem      24.1.5
$\hat{A}$ -class      24.3
$\hat{A}$ -genus      24.3.2
$\sigma$ -additive theory      21.1.1
$\sigma$ -unital C*-algebra      12.3
a-T-menable group      24.2.3(d)
Absorbing extension      15.12.1
Absorption Theorem      13.6.2 14.6.1 20.1.3
AF algebra      7.1.1
Algebraic equivalence      4.2.1
Algebraic K-theory      1.7.3
Amalgamated free product      10.11.11
Arens — Royden theorem      9.4.3
Assembly map      24.4
Asymptotic morphism      25.1.1
Atiyah — Singer index theorem      24.1.1
B-vector bundle      24.1.4
Baaj — Julg picture      17.11
Baum — Connes conjecture      24.4
Bootstrap category      22.3.4
Bott element      9.2.10 19.2.5
Bott map      9.1.1
Bott periodicity      1.6.4 2.3 2.4 2.5 9.2.1 11.9.4 15.11.1 19.2.2 20.3
Bott projection      9.2.10
Bratteli diagram      7.2
Brown — Green — Rieffel Theorem      13.7.1
Bunce — Deddens algebra      10.11.4
Bushy invariant      15.2
Calkin algebra      2.3
Cancellation      1.2.1 6.4
Canonical elements      19.2 19.9.3 19.9.4 20.7
CAR algebra      7.5
Characteristic number      24.2
Chern character      1.6.6
Choi algebra      6.10.5
Classifying map      24.2
Classifying space      24.2
Clifford algebra      1.6.4 14.1.2
Clutching      1.1.2
Cobordism      17.10
Cohomology theory      21.1.1
Cohomotopy      18.13.2
Completely additive theory      21.1.1
Connection      18.3
Connes — Kasparov-Rosenberg conjecture      20.7.6
Connes' Thom Isomorphism      10.2.2 19.3.6
Continuity axiom      21.3
Continuous functor      21.3
Coproduct property      22.1.1
Correspondence      19.9.6
Covariant representation      10.1
Covariant system      10.1
Crossed product      10.1
Cuntz algebra      6.3.2 10.11.8
Cuntz picture      17.6
Cuntz — Krieger algebra      10.11.9
de la Harpe — Skandalis determinant      10.10.1
Degenerate Kasparov module      17.1.1
Dimension axiom      22.3
Dimension function      6.9
Dimension group      7.3
Dirac operator      17.1.2(g)
Direct limit      3.3
Dolbeault element      17.1.2(f)
Dual action      10.1
Dynamical system      10.1
Effros — Handelman — Shen Theorem      7.4.1
Equivalence (of extensions)      15.4
Equivalence (of idempotents)      4.2.1
Essential extension      15.2
Essential homomorphism      13.5.2 17.8.2(a)
Essential spectrum      16.2
Essentially n-normal operator      16.4.2
Essentially normal operator      16.2
Even grading      14.1.1
Exact C*-algebra      23.13
Exact sequence      5.6.1
Excision      22.4.3 22.4.4
Exponential map      9.3.2
Extendibility      18.11
Extension      2.4 15.1.1
External tensor product      13.5.1 14.4.4
Factors, K-theory of      2.2 5.1.3 5.3.2
Fibered product      1.1.3
Finite algebra      6.3.2
Formal Bott Periodicity      17.8.9 20.2.5
Fredholm module      17.5
Fredholm picture      17.5
Frobenius reciprocity theorem      20.5.5
Full Hilbert module      13.1.1
Functional dual spectrum      16.4.4
G-continuous operator      20.1.2
G-vector bundle      11.4
Generalized integer      7.5
Generalized Kadison conjecture      24.4
Generalized signature      24.2.2
Generalized Stinespring Theorem      13.7.2
Generalized Toeplitz algebra      19.9.2
Geometric resolution      23.5
Graded C*-algebra      14.1.1
Graded commutator      14.1.1
Graded covariant system      20.1.3
Graded Hilbert module      14.2
Graded homomorphism      14.1.1
Graded tensor product      14.4
Grading automorphism      14.1.1
Grading operator      14.1.1
Grassmann connection      18.3.2(b) 18.3.3
Green — Julg Theorem      11.7.1 20.2.7
Grothendieck group      1.3
Gysin map      17.1.2(g)
Half-exact functor      21.4
Heisenberg group      16.4.3
Higher A-genus      24.3.3
Higher signature      24.2
Hilbert module      13.1.1
Hilbert space over B      13.1.2
Homogeneous element      14.1.1
Homogeneous state      14.1.1
Homology theory      21.1.1
Homotopy (of extensions)      15.4
Homotopy (of homomorphisms)      5.2.2
Homotopy (of idempotents)      4.2.1
Homotopy (of Kasparov modules)      17.2.2
Homotopy axiom      21.1
Idempotent      4.1.1
Index map      8.3.2
Index theorem      24.1
Index theorem for families      24.1.3
Induction homomorphism      20.5.4
Inductive limit      3.3
Injective resolution      23.5
Internal tensor product      13.5.1 14.4.2
Intersection product      18.1 20.3
Irrational rotation algebra      10.11.6
Isometry      4.6.1
K-amenable group      20.9.1
K-contractible      19.1
K-homology      16.3
K-nuclear C*-algebra      20.10.2
K-theory mod p      23.15.7
K-theory with rational coefficients      23.15.6
Kasparov G-module      20.2.1
Kasparov module      17.1.1
Kasparov product      18.4.1
Kasparov's Technical Theorem      12.4.2 14.6.2 20.1.5

KK-domination      23.10.6
KK-equivalence      19.1.1
Kleisli category      22.1
Kuenneth theorem      23.1.2
Kuenneth Theorem for Tensor Products      23.1.3
Lim-sequence      21.3.2 21.5.2
Line bundle      1.1.1
Local Banach algebra      3.1.1
Local C*-algebra      3.1.1
Long Exact Sequence      1.6 8.3 21.1.1
Longitudinal index theorem      24.1.6
Mapping cone      15.3 19.4.2(b)
Mapping torus      10.3.1 20.5.3
Matroid C*-algebra      7.5
Mayer — Vietoris sequence      21.2 21.5.1
Milnor lim-sequence      21.3.2 21.5.2
Miscenko — Fomenko Index Theorem      24.1.4
Morita equivalence      13.7.1
Multiplier algebra      12.1
Murray-von Neumann equivalence      4.6.4
n-normal operator      16.4.2
Noncommutative differential geometry      24.1.8
Noncommutative topology      2.1
Noncommutative torus      10.11.6
Nonstable K-theory      6.5
Normed inductive limit      3.3
Novikov conjecture      24.2.1
Nuclear C*-algebra      15.8.1
Odd grading      14.1.2
Operator homotopy      17.2.2
Order ideal      6.2.1
Order unit      6.2.1
Ordered group      6.2.1
Ordinary ordering      6.2.2
Orthogonal idempotents      4.1.1
Outer multiplier algebra      12.1
Outer tensor product      13.5.1 14.4.4
Partial isometry      4.6.1
Pedersen ideal      3.1.2
Perforation      6.7.1
Pimsner — Voiculescu exact sequence      10.2.1 16.4.5 19.6.1
Polar decomposition      3.1.7
Poorly infinite C*-algebra      6.10.1
Positive scalar curvature      24.3
Pre-Hilbert module      13.1.1
Preordered group      6.1
Prequasihomomorphism      17.6.2
Projection      4.6.1
Projective module      1.7.1
Projective resolution      23.5
Properly infinite C*-algebra      6.11.1
Pullback      15.3
Puppe sequence      19.4.3
Purely infinite C*-algebra      6.11.4
Quasicentral approximate identity      12.4
Quasihomomorphism      17.6.2
Quasihomomorphism picture      17.6
Quasitrace      6.9
Real C*-algebra      19.9.7
Real rank zero      6.5.6
Reduced crossed product      10.1
Regular operator      13.3.1
Relative homology theory      22.4.3
Relative K-group      1.5 5.4
Representation ring      11.1.3 20.4.2
Residually essential extension      15.12.4
Restriction homomorphism      20.5.1
Riemann — Roch theorem      24.1.2(b)
Riesz interpolation property      7.4
Ring structure on K      1.7.5
Ring structure on KK      18.8 20.4.1 23.11.1
SCALE      6.1
Scaled ordered group      6.2.1
Scaled preordered K0-group      6.1
Section      1.1.2
Semiprojective C*-algebra      4.7.1
Semisplit extension      19.5.1
Shilov Idempotent Theorem      9.4.3
Shriek map      17.1.2(g)
Signature      24.2
Similarity      4.2.1
Simple ordered group      6.2.1
Singular space      2.1
Split exact sequence      15.5
Splitting morphism      17.1.2(b)
Stabilization theorem      13.6.2 14.6.1 20.1.3
Stable algebra      5.1.1
Stable equivalence (of extensions)      15.6.3
Stable isomorphism      5.1.2
Stable multiplier algebra      12.1.3
Stable outer multiplier algebra      12.1.3
Stable rank      6.5
Stable theory      21.1.1
Stably finite algebra      6.3.2
Stably unital Banach algebra      5.5.4
Standard even grading      14.1.2 14.2
Standard exact sequence      9.3 19.5.7
Standard homotopy      17.2.2
Standard odd grading      14.1.2
State (on ordered group)      6.8.1
Stinespring theorem      13.7.2
Strict ordering      6.2.2
Strict topology      12.1
Strictly positive element      12.3
Strong equivalence (of extensions)      15.4
Strong excision      22.4.3
Strong isomorphism (of extensions)      15.4
Strong Novikov conjecture      24.2.2
Strongly unital trivial extension      15.5
Suspension      1.6.1 1.7.4 8.2.1
Swan's Theorem      1.2.2
Symbol      24.1
Takai Duality Theorem      10.1.2
Technical Theorem (Kasparov)      12.4.2 14.6.2 20.1.5
Thom element      19.3.3
Thom Isomorphism (Connes)      10.2.2 19.3.6
Thom Isomorphism (topological)      10.2 19.9.4
Thom module      19.3
Thom operator      19.3.1
Toeplitz algebra      9.4.2
Toeplitz extension      10.2 19.9.2
Topological Markov chain      10.11.9
Trace      6.9
Trivial bundle      1.1.1
Trivial extension      15.5
Trivial grading      14.1.1
Twice-around embedding      10.11.4
Twisted crossed product      10.1
UHF algebra      7.5
Ultrasimplicially ordered group      7.7.2
Unbounded Kasparov module      17.11.1
Unital-absorbing extension      15.12.1
Unitary      4.6.1
Unitary equivalence      4.6.5
Unitization      3.2
Universal coefficient theorem      16.3.3 23.1.1
Unperforated ordered group      6.7.1
Vector bundle      1.1.1
Very full projection      6.11.7
Voiculescu's Theorem      15.12.3
Weak equivalence (of extensions)      15.4
Weak excision      22.4.3
Weak isomorphism (of extensions)      15.4
Weakly unperforated ordered group      6.7.1
Well-supported element      6.5.3
Weyl — von Neumann theorem      16.2.3
Whitehead lemma      3.4.1
Whitney sum      1.2
Wiener — Hopf extension      10.9

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