Connes A. — Noncommutative geometry :: Электронная библиотека попечительского совета мехмата МГУ

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Connes A. — Noncommutative geometry

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Название: Noncommutative geometry

Автор: Connes A.

Аннотация:

This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.

Key Features
* First full treatment of the subject and its applications
* Written by the pioneer of this field
* Broad applications in mathematics
* Of interest across most fields
* Ideal as an introduction and survey
* Examples treated include:
@subbul* the space of Penrose tilings
* the space of leaves of a foliation
* the space of irreducible unitary representations of a discrete group
* the phase space in quantum mechanics
* the Brillouin zone in the quantum Hall effect
* A model of space time

Язык:

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 661

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Longitudinal index theorem      II.9. $\gamma$
Longitudinal signature      II.9. $\beta$
Lorentz space      IV.3. $\gamma$ —IV.B
Macaev ideal      IV.C
Markov trace      V.10. $\beta$
Matricially ordered space      V.7
Matrix mechanics      I.1
Maximal compact subring      V.11. $\gamma$
Mean oscillation      IV.3. $\alpha$
Measurable operator      IV.2. $\delta$
Measured equivalence relation      V.4
Minkowski dimension      IV.3. $\beta$
Minkowski measurable      IV.3. $\beta$
Minkowski measure (or content)      IV.3. $\beta$
Mishchenko line bundle      II.4
Mock discrete series      IV.3. $\alpha$
Modular automorphism group      V.3
Modular operator      V.5
Modular spectrum      V.8. $\delta$
Module of automorphism      V.8. $\gamma$
Module of local field      V.1. $\gamma$
Morse function      1.5. $\delta$ —IV.9. $\alpha$
Multiplier (of C*-algebra)      II.C
n-trace      III.6. $\alpha$
Nerve (of small category)      III.A. $\alpha$
Non-exponential growth (foliation)      I.A
Noncommutative Brillouin zone      IV.6. $\gamma$
Noncommutative space      II.3
Noncommutative torus      III.2. $\beta$ —IV.6. $\alpha$ —VI.3.C
Normal linear functional      V.2
Normal weight      V.3
Normalized cocycle (in entire cyclic cohomology)      IV.7. $\alpha$
Normalized group cocycle      III.1. $\alpha$
Normalized Kasparov bimodule      IV.A
Normalizer (of abelian subalgebra)      V.4
Normed ideal      IV.C
Novikov conjecture      II.4
Nuclear C*-algebra      V.7
Obstruction $\gamma$       V.6. $\varepsilon$
Odd (Fredholm module)      IV
Operator-valued distribution      IV.8. $\beta$
Operatorial homotopy      IV.A
Order of de Rham current      III.6. $\alpha$
Order-one condition (on K-cycle)      VI.4. $\gamma$
Orientation in KO-homology      VI.4. $\alpha$
Outer conjugate automorphisms      V.6
Outer equivalent actions (on C* -algebra)      II.C
Outer equivalent actions (von Neumann algebras)      V.A—V.5—V.6
p-adic integers      V.ll. $\gamma$
p-adic numbers      V.ll. $\gamma$
Pairing of cyclic cohomology with K-theory      III.3
Pairing of entire cyclic cohomology with K-theory      IV.7. $\delta$
Paneitz operator      IV.4. $\gamma$
Penrose tilings      II.3—II.D
Perfect set      IV.3. $\varepsilon$
Periodic cyclic cohomology      III.3—III.1. $\gamma$
Perturbation of Fredholm module      IV.4. $\beta$
Places      V.ll. $\gamma$
Plaque      1.4. $\beta$
Poincare duality (in K-theory)      VI.4. $\beta$
Poincare series      IV.3. $\delta$ —lV.3. $\varepsilon$ —IV.5
Poisson bracket      IV.D
Polyakov action      IV.4. $\gamma$
Polynomial map (of K theory)      IV.9. $\beta$
Pontryagin dual      II.4
Positive element (of a C*-algebra)      V.2
Positive Hochschild cocycle      VI.2
Positive linear form      V.2
Positivity in Hochschild cohomology      VI.2
Postliminal C*-algebra      V.2
Powers factors      V.4
Powers-Stormer inequality      IV.9. $\alpha$
Pre-C*-algebra      IV.l. $\gamma$
Pre-C*-module      II.A
Predual (of von Neumann algebra)      V.1
Projection      I.4. $\gamma$
Projective module of finite type      II.1
Proper (action of group)      II.7
Proper (action of groupoid)      II.8—II.10. $\alpha$
Proper G-manifold      II.10. $\alpha$
Proper smooth groupoid      II.10. $\alpha$
Properly infinite representation      V.I
Property E of Hakeda and Tomiyama      V.7. $\beta$
Property P of Schwartz      V.7. $\beta$
Property r      V.I
Property T (locally compact group)      II.10. $\delta$
Property T (von Neumann algebra)      V.B. $\varepsilon$
Pure gauge boson      VI.3.b—VI.5. $\beta$
Pure state      V.2
q-analogue      IV.6. $\alpha$
Quadratic form on a Hilbert space      V.5
Quantized calculus      IV
Quantum field theory      IV.9. $\beta$
Quantum Hall effect      IV.6. $\beta$
Quantum space      II.3
Quasi-central approximate unit      II.B—IV.2. $\delta$
Quasi-continuous function      IV.3. $\alpha$
Quasi-Fuchsian circle      IV.3. $\gamma$
Quasi-Fuchsian group      IV.3. $\gamma$
Quasi-invariant measure      V.4
Quasi-isomorphism      II.9. $\alpha$
Quasi-nilpotent (element of algebra)      IV.7. $\beta$
Quasi-nilpotent extension      IV.7. $\beta$
Quasicontinuous (element of von Neumann algebra)      IV.6. $\gamma$
Quaternion      VI.5. $\delta$
Radon — Nikodym theorem      V.5. $\alpha$
Random form      V.5
Random operator      I.4. $\gamma$ —V.1. $\alpha$
Real Betti number      I.5. $\delta$

Real interpolation (of Banach spaces)      IV.B
Reduced C*-algebra      II.A
Reduced crossed product of C* -algebra      II.C
Reduced dual (of a discrete group)      II.4
Reduced groupoid      II.8
Reduced representation      V.1. $\gamma$
Reduced universal differential algebra      VI.1
Reduced von Neumann algebra      1.4. $\gamma$
Reduction theory (of von Neumann)      V.I. $\beta$
Relative cyclic cohomology      III.1. $\gamma$
Relative dimension function      V.1. $\gamma$
Relative entropy      V.6. $\beta$
Relative Lie algebra cohomology      II.10. $\gamma$
Residual field      V.1. $\gamma$
Residue formula      IV.2. $\gamma$
Residue of pseudodifferential operator      IV.2. $\beta$
Riesz representation theorem      V.2
Ritz — Rydberg combination principle      I.1
Ruelle-Sullivan cycle      I.5. $\beta$
Scale invariance      IV.2. $\beta$
Schatten — von Neumann ideal      IV
Self-similarity      V.9
Selfadjoint operator      I.4. $\alpha$
Semi-discrete von Neumann algebra      V.7
Semifinite von Neumann algebra      I.4. $\gamma$
Semifinite weight      V.3
Shift automorphism      V.6
Simple (C*-algebra)      II.1
Simplicial category      III.A. $\alpha$
Simplicial object      III.A. $\alpha$
Smash product (of spaces)      II.B
Smooth groupoid      II. $\delta$
Smooth groupoid of a covering space      III.4. $\alpha$
Spatial isomorphism      V.1
Spectrum (Atomic)      I.1
Spectrum (in algebraic topology)      II.B
Spectrum (of automorphism group)      V.5
Spectrum (of C*-algebra)      II.1
Spin structure      II.6. $\gamma$
Stability of Fredholm module      IV.4. $\delta$
Stability under holomorphic functional calculus      III.C
Stabilization theorem (C*-modules)      II.A
Standard model      VI.5. $\beta$
Star operation (conformal)      IV.4. $\alpha$
Star product      IV.D
State of a C*-algebra      V.2
Statistical state      I.2
Steenrod generalized homology      II.B
Strong Morita equivalence      II.A
Strong Novikov conjecture      II.4
Subfactor of finite index      V.10. $\alpha$
Subfactors      V.10
Super group      IV.8. $\beta$
Supercharge operator      IV.9. $\beta$
Superconnection      IV.A
Supersymmetry      IV.9. $\beta$ —IV.8. $\beta$
Symmetrically normed ideal      IV.C
Symmetrically norming function      IV.C
Takesaki duality      V.A.
Takesaki — Takai duality      II.C
Tangent groupoid (of manifold)      II. 5
Tensor product of C*-modules      II.A
Tensor product of cycles      III.1. $\alpha$
Thorn isomorphism (for C* -algebras)      II.C
Toeplitz C*-algebra      II.B
Topological G-index      II.10. $\alpha$
Topological module      III.B
Topological projective module      III.B
Topological resolution      III.B
Trace      I.4. $\gamma$ —V.I
Transversal (of foliation)      I.5. $\alpha$
Transverse differentiation      III.7. $\alpha$
Transverse fundamental class (foliations)      III.7. $\alpha$
Transverse measure      I.5. $\alpha$
TREE      IV.5
Tree of SL(2)      V.ll. $\gamma$
Twisted cohomology (for etale smooth groupoid)      III.2. $\delta$
Twisted cohomology (for group action)      III.2. $\delta$
Type I (von Neumann algebra)      I.4. $\gamma$
Type II (von Neumann algebra)      I.4. $\gamma$
Type III (von Neumann algebra)      I.4. $\gamma$
Ultrametric      V.ll. $\gamma$
Ultraproduct      V.6
Unbounded endomorphism of C*-module      IV.A
Unbounded operator (Banach space)      III.6. $\alpha$
Unimodularity      VI.5. $\varepsilon$
Unitary automorphism (on Hermitian projective module)      VI.1
Unitary group (of involutive algebra)      VI.5. $\alpha$ —VI. 1
Universal compatible connection      VI.1
Universal connection      VI.1
Universal differential algebra      III.1. $\alpha$
Vacuum representation      IV.9. $\beta$
Vacuum vector      IV.9. $\beta$
Vanishing cycle      III.1. $\alpha$
Vanishing mean oscillation      IV.3. $\alpha$
Vector potential      VI.1
Virtual group      V.8. $\delta$
von Neumann algebra      V.1
Von Neumann algebra (of a foliation)      1.4. $\gamma$
Weak normalization (of entire cocycles)      IV.7. $\varepsilon$
Weakly equivalent transformations      V.4
Wedge (of spaces)      II.B
Weight (on a von Neumann algebra)      V.3
Wess — Zumino model      IV.9. $\beta$
Witt group      II.1
Wodzicki residue      IV.2. $\beta$
Wrong way functoriality      II.6
Yang — Mills action      VI.1
Yukawa coupling      VI.3. $\beta$ —VI.5. $\beta$

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