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Rordam M., Stormer E. — Classification of Nuclear C*-Algebras Entropy in Operator Algebras
Rordam M., Stormer E. — Classification of Nuclear C*-Algebras Entropy in Operator Algebras



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Название: Classification of Nuclear C*-Algebras Entropy in Operator Algebras

Авторы: Rordam M., Stormer E.

Аннотация:

This EMS volume consists of two parts, written by leading scientists in the field of operator algebras and non-commutative geometry. The first part, written by M.Rordam, is on Elliott's classification program for nuclear C*-algebras. The emphasis is on the work of Kirchberg and the spectacular results by Kirchberg and Phillips giving a nearly complete classification, in terms of K-theoretic invariants, in the purely infinite case. This part of the program is described with almost full proofs beginning with Kirchberg's tensor product theorems and Kirchberg's embedding theorem for exact C*-algebras. The classification of finite simple C*-algebras starting with AF-algebras, and continuing with AT- and AH-algebras is covered, but mostly without proofs. The second part, written by E.Stormer, is a survey of the theory of of noncommutative entropy of automorphisms of C*-algebras and von Neumann algebras from its initiation by Connes and Stormer in 1975 till 2001.


Язык: en

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 415

Добавлена в каталог: 14.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(a-\varepsilon)_{+}$      68
$1_{A}$      35
$Inn_{0}(-)$      52
$K_{0}$      9
$K_{0}$, $K_{0}(-)$      9 67
$K_{0}$, $K_{0}(-)^{+}$      9
$K_{0}$, $K_{0}(\tau)$      10
$K_{0}$, $[\cdot]_{0}$      9
$K_{0}$, $\mathcal{D}_{0}(-)$      10
$K_{0}$, cancellation property      11
$K_{0}$, dimension range      10
$K_{1}$      50
$K_{1}$, $K_{1}(-)$      50 67
$K_{1}$, $[\cdot]_{1}$      50
$K_{1}$-injective      86
$K_{\ast}(-)$      29 50 61
$K_{\ast}(-)$, $K_{\ast}(-)^{+}$      29
$K_{\ast}(-)$, $\mathcal{D}_{\ast}(-)$      50
$M_{2^{\propto}}$      16
$M_{n}$      16
$RR(-)=0$      9
$r_{A}$      10 27 45
$sr(-)=1$      9
$\kappa_{A,B}$      121
$\mathbb{T}$      48
$\mathbf{KK}$      36
$\mathcal{BD}$      44
$\mathcal{D}(k)$      44
$\mathcal{D}_{0}(-)$      10
$\mathcal{K}$      7
$\mathcal{M}(-)$      11 110
$\mathcal{N}$      38 127
$\mathcal{N}_{nuc}$      38
$\mathcal{O}_{2}$      70 86ff 109
$\mathcal{O}_{A}$      78 81
$\mathcal{O}_{e}$      82
$\mathcal{O}_{n}$      70
$\mathcal{O}_{\propto}$      70 113
$\mathcal{P}(-)$      9
$\mathcal{Q}$      16
$\mathcal{Q}(n)$      16
$\mathcal{SDG}$      44
$\mathcal{T}$      82
$\mathcal{U}(-)$      50 67
$\mathcal{U}(-)_{0}$      50 52
$\mathcal{Z}$      63
$\otimes_{max}$      24
$\otimes_{min}$      24 93
$\overline{Inn}(-)$      11
$\overline{Inn}_{0}(-)$      52
$\overline{Inn}_{h}(-)$      132
$\smile\rho\parallel_{cb}$      91
$\widehat{H}(-,-)$      120
(F0)      26
(Fl)      26
(FU)      67
(Inf)      26
(IP)      23
(SP)      46
(SP), property      46
*-homomorphism, $\mathcal{O}_{2}$-absorbing      116
*-homomorphism, $\mathcal{O}_{\propto}$-absorbing      116
*-homomorphism, $\varphi\approx_{uh}\psi$      12
*-homomorphism, $\varphi\approx_{u}\psi$      11
*-homomorphism, $\varphi\oplus\psi$      114
*-homomorphism, $\varphi\sim_{h}\psi$      11
*-homomorphism, $\varphi\sim_{u}\psi$      11
*-homomorphism, approximate unitary equivalence      11
*-homomorphism, asymptotic unitary equivalence      12
*-homomorphism, asymptotically central      90
*-homomorphism, full      115
*-homomorphism, homotopy      11
*-homomorphism, unitary equivalence      11
Abelian group, ordered      9
Abelian group, preordered      9
Ad u      11
AF-algebra      12 12
AH-algebra      43 ff 58
AH-algebra, bounded dimension      44
AH-algebra, slow dimension growth      44
Al-algebra      49
Amenable      25
Approximate divisibility      47 113
Approximate intertwining      30ff
Approximate unitary equivalence      11
Approximately subhomogeneous C*-algebra      62
ASH-algebra      62 62ff
Asymptotic morphism      118
Asymptotic morphism, asymptotically unitarily equivalent      118
Asymptotic morphism, homotopic      118
Asymptotic morphism, scaling      119
Asymptotic unitary equivalence      12
Asymptotically central sequence      90
AT-algebra      48 48
Aut(-)      11
Automorphism      11
Automorphism, approximately inner      11
Automorphism, inner      11
Bernoulli shift      87
Bootstrap class      38
Bratteli diagrams      13ff
Bunce — Deddens algebra      53 56
C*(E)      79
C*-alg      36
C*-algebra, $(A)_{\propto}$      95
C*-algebra, $A_{\omega}$      96
C*-algebra, $l_{\propto}(A)$      95
C*-algebra, $\mathcal{M}(A)$      11
C*-algebra, $\widetilde{A}$      11
C*-algebra, amenable      25
C*-algebra, approximately divisible      47
C*-algebra, approximately inner automorphism      11
C*-algebra, automorphism      11
C*-algebra, classifiable      40 76 115
C*-algebra, exact      8 10 76 91 94
C*-algebra, finite      7
C*-algebra, finite dimensional      12
C*-algebra, ideal property      23
C*-algebra, infinite      7
C*-algebra, inner automorphism      11
C*-algebra, K-abelian      38
C*-algebra, nuclear      24 91
C*-algebra, properly infinite      7
C*-algebra, purely infinite      66 66ff
C*-algebra, quasidiagonal      48 106
C*-algebra, semiprojective      13 134
C*-algebra, stably finite      7 8 10
C*-algebra, stably projectionless      7
C*-algebra, tensorial non-prime      69
C*-algebra, tensorial prime      69
C*-algebra, tracial topological rank zero      59
C*-algebra, ultrapower      96
C*-algebra, unitization of      11
Cancellation property      11
Canonical anticommutation relations      16 87
CAR-algebra      16 55 87
CAR-algebra, even subalgebra      87
Choquet simplex      10 23
Circle algebra      48
Complete contraction      92
Completely bounded map      91
Completely positive map      92
Corner endomorphism      76
Cuntz algebra      70ff
Cuntz relation      70
Cuntz sum      40 114
Cuntz — Krieger algebra      78
Cuntz — Krieger algebra, generalized      79 81
CW-complex      43
Dimension drop C*-algebra      58 64
Dimension group      20
Dimension range      10
Dynamical system      54
e-Theory      122
Eigenvalue functions      45
Elliott conjecture      25ff
Elliott conjecture, finite case      28
Elliott conjecture, infinite case      26
Elliott conjecture, real rank zero case      30
Elliott invariant      29
Elliott invariant, finite case      28
Elliott invariant, infinite case      27
Elliott invariant, real rank zero case      30
Exact C*-algebra      8 10 76 91ff
Excising states      68 98
Existence theorem      41
Exponential length      86
Filter      95
Filter, free      96
Filter, free ultrafilter      96
Filter, ultrafilter      96
Finite C*-algebra      7
Finite dimensional C*-algebras      12
Finite projection      7
Free ultrafilter      96
Functor, half exact      37
Functor, homotopy invariant      36
Functor, natural transformation      36
Functor, split exact      36
Functor, stable      36
Goodearl algebras      46
Graded dimension range      50
Graded K-group      50
H(-,-)      40
Homotopic *-homomorphisms      11
Ideal property      23
Infinite C*-algebra      7
Infinite projection      7
Inn(-)      11
Intertwining      31
Jiang-Su algebra      63
Kasparov product      35
Kirchberg algebra      75
Kirchberg’s Weyl-von Neumann Theorem      126
kk      34ff
KK, $KK(-,-)^{-1}$      37
KK, $KK(\varphi)$      35
KK, KK(-,-)      34
KK-equivalence      37
KK-theory      34ff
KL      39
KL-group      39
Limit algebras      95ff
Local $A\mathbb{T}$-algebra      49
Local AF-algebra      12
Local AH-algebra      47
Minimal Cantor system      54
Multiplier algebra      11
Nuclear C*-algebra      24ff 91ff
Nuclear map      92
Operator space      91
Operator system      91
Order unit      9
Ordered abelian group      9
Ordered abelian group, ideal      22
Ordered abelian group, order unit      9
Ordered abelian group, simple      9
Ordered abelian group, state space      9
Ordered abelian group, weakly unperforated      58
Paradoxical group      83
Pi-sun algebras      75
Pimsner algebras      82
Preordered abelian group      9
projection, $\oplus$      7 11
projection, $\precsim$      7 23
projection, $\sim$      7 11
Projection, comparison      23
Projection, finite      7
Projection, full      67
Projection, infinite      7
Projection, properly infinite      7
Proper corner endomorphism      76
Properly infinite projection      7
Purely infinite C*-algebra      66
Purely infinite C*-algebra, classifiable      40
Quasi-homomorphism      34
Quasidiagonal C*-algebra      48
Quasitrace      8 10
Real rank zero      9
Riesz group      21
Riesz interpolation property      21
Rokhlin property      87
Rokhlin tower      87
Semiprojective      13 49
Semiprojective C*-algebra      134
Slow dimension growth      44
Stability of an endomorphism      88
Stable rank one      9 29
Stable relations      49
Stably finite C*-algebra      7 8 10
Standard factorization      116
Stinespring’s Theorem      92
Subhomogeneous C*-algebra      62
Supernatural number      15
T(-)      8
TAF-algebras      59
Toeplitz algebra      8 50
tr      14
Trace      8
Tracial state      8
Tracial topological rank zero      59
Twice around embedding      53
UCT      38
UCT class $\mathcal{N}$      38
UCT class $\mathcal{N}_{nuc}$      38
UHF-algebra      15
Ultrafilter      96
Ultrafilter, free      96
Ultrapower C*-algebra      96
Uniqueness theorem      41 86
Unitary equivalence      11
Universal coefficient theorem      38
Unperforation      21
Weakly nuclear map      125
Weakly unperforated      58
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