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

$\Lambda$ -module      III.A. $\gamma$
$\theta$ -summable (Fredholm module)      IV
$\theta$ -summable K cycle      IV.8
Abelian projection      1.4. $\gamma$
Abelian von Neumann algebra      V.I
Adeles      V.ll. $\gamma$
Adjoint operator      II.6. $\alpha$
Algebraic isomorphism (of von Neumann algebras)      V.I
Algebraically contractible (algebra)      III.L. $\alpha$
Almost equivariant map      IV.5
Almost normal subgroup      V.ll. $\alpha$
Amenable von Neumann algebra      V.7
Anabelian 1-trace      III.6. $\gamma$
Analytic assembly map (for foliation)      II.8. $\gamma$
Analytic assembly map (for group action)      II.7
Analytic assembly map (smooth groupoids)      II.10. $\alpha$
Aperiodic automorphism      V.6
Approximately inner automorphism      V.6. $\gamma$
Approximately transitive (ergodic group action)      V.9. $\delta$
Araki — Woods factors      V.4
Asymptotic centralizer      V.6
Asymptotic morphisms (of C*-algebras)      II.B
Asymptotic period      V.6
Asymptotic ratio set      V.4
Atomic spectrum      I.1
Averaging sequence      l.A.
Bar resolution      IV.7. $\varepsilon$ —lll.2. $\alpha$
Beltrami differential      IV.4. $\beta$
Besov space      IV.3. $\alpha$
Bicomplex (b,B)      Ill.1. $\gamma$
Binormal representation      V.B. $\gamma$
Binormal state      V.B. $\gamma$
Bivariant theory (Kasparov)      IV.A
Bivector potential      VI.4.5
Bosonic Hilbert space      IV.9. $\beta$ —V.11. $\beta$
Bott periodicity      II.1
Bott — Thurston cocycle      II.6. $\beta$
Boundary of chain      III.1. $\beta$
Bounded group cocycle      III.5. $\gamma$
Bounded mean oscillation      IV.3. $\alpha$
Bounded variation (function)      III.6. $\alpha$
Bounded vector      V.B. $\gamma$
Bra-ket notation      II.A
Broken symmetry      VI.3. $\alpha$ —V.ll. $\alpha$
C*-algebra      II.1
C*-algebra index      II.9. $\beta$
C*-algebra of foliation      II.8. $\alpha$
C*-algebra of smooth groupoid      II.5
C*-module      II.A
Cantor set      IV.3. $\varepsilon$
Cartan subalgebra (of von Neumann algebra)      V.4
Causality (in quantum field theory)      IV.9. $\beta$
Center (of von Neumann algebra)      1.4. $\gamma$
Centralizer (of group element)      III.2. $\gamma$
Centrally trivial automorphism      V.6. $\delta$
Cesaro mean      IV.2. $\beta$
Chain      III.1. $\beta$
Character of cycle      III.I. $\alpha$
Characteristic values (of compact operator)      IV.2. $\alpha$ —IV.C
Chern character (of Fredholm module)      IV.1. $\beta$
Chern character of Fredholm module $\theta$ -summable case)      IV.8
Classifying space (for discrete group)      II.7—III.2. $\gamma$
Classifying space of topological groupoid      II.8—III.A
Closable operator      III.6. $\alpha$
Closed star product      IV.D
Closed transversal (of foliation)      II.8
Closedness condition      VI.4. $\gamma$
Closure of operator      III.6. $\alpha$
Coarse correspondence      V.B. $\beta$
Cobordism of cycles      III.1. $\beta$
Cocycle J.L.O.      IV.8. $\varepsilon$
Cocycle Radon — Nikodym theorem      V.5
Coefficient of correspondence      V.B. $\gamma$
Color group      VI.5. $\beta$
Combination principle (Ritz — Rydberg)      I.1
Commutant (in Hilbert space)      V.1
Compact endomorphism (of C* module)      II.A
Compatible connection      VI.1
Completely positive map      V.6.K
Complex Hilbert transform      IV.4. $\alpha$
Complex interpolation (of Banach spaces)      IV.B
Composition of asymptotic morphisms      II.B
Composition of correspondences      V.B.5
Cone of a map      II.B
Configuration space (for discrete group)      III.2. $\gamma$
Conformal manifold      IV.4
Conjugate automorphisms      V.6
Connection (in KK-theory)      IV.A
Connection (over a cycle)      III. 3
Connection (over a K-cycle)      VI. 1
Constructive quantum field theory      IV.9. $\beta$
Continuous decomposition      V.8. $\beta$
Continuous field of Banach spaces      II.A
Continuous multilinear form      III.B
Contractible C*-algebra      II.5
Contraction of cyclic cocycle      III.6. $\beta$
Contragredient correspondence      V.8. $\beta$
Coproduct      IV.8. $\beta$
Correspondence (von Neumann algebras)      V.B
Covariant representation (of C* -algebra)      II.C
Creation operator      lV.9. $\beta$
Crossed product (of C*-algebra)      II.C
Crossed product of von Neumann algebra      V.A
Cuntz algebra      IV.7. $\gamma$
Cup product (in cyclic cohomology)      III.1. $\alpha$
Cycle (over an algebra)      III.1. $\alpha$
Cyclic category      III.A
Cyclic cohomology      III.1. $\alpha$
Cyclic object      III.A. $\beta$
Cyclic space      III.A
De Rham current      1.5. $\alpha$
Deformation (of C*-algebras)      II.B
Deformation of algebras      IV.D
Deformations (Lie groups)      II.1O. $\beta$
Degeneracy map      III.A. $\alpha$
Degenerate Kasparov bimodule      IV.A
Degenerate quasi-isomorphism      II.9. $\alpha$
Degree of summability (of Fredholm module)      IV.2. $\delta$
Densely defined cyclic cocycle      III.6. $\alpha$
Densely denned operator      III.6. $\alpha$
Densely summable (Fredholm module)      IV.l. $\gamma$
Density theorem      III.C
Derivation (Banach algebra, bimodule)      III.6. $\varepsilon$
Determinant      VI.5. $\varepsilon$
Differential component      VI.5. $\delta$
Differential degree      VI.3.b
Dihedral group      II.2. $\beta$
Diophantine condition      III.2. $\beta$
Dirac element (of KK-theory)      IV.A
Dirac induction (Lie groups)      II.10. $\gamma$
Direct integral      V.1
Discrete decomposition (III case)      V.8. $\alpha$
Discrete decomposition (III $_{\lambda}$ case)      V.5. $\beta$
Dixmier trace      IV.2. $\beta$
Dominant weight      V.8. $\gamma$
Dual Dirac element (of KK-theory)      IV.A
e-Theory      II.B
Elementary C * -algebra      II. 5
Endomorphism of C* module      II.A
Entire cochain      IV.7. $\alpha$
Entire cyclic cohomology      IV.7. $\alpha$
Entire cyclic cohomology of $\mathbb{S}^1$       IV.7. $\varepsilon$
Entropy defect      V.6. $\beta$
Entropy of automorphism      V.6. $\beta$
Equivalent asymptotic morphisms      II.B
Equivalent projections      II.3—V.I
Equivalent representations      I.1
Equivalent semifinite normal weights      V.8. $\gamma$
Equivariant cohomology (for compact group)      III.2. $\gamma$
Equivariant index (for discrete group)      III.4. $\beta$

Equivariant Kasparov bimodule      IV.A
Etale smooth groupoid      III.2. $\delta$
Euler characteristic      1.5. $\beta$
Euler number of measured foliation      1.5. $\beta$
Even (Fredholm module)      IV
Excision (in cyclic cohomology)      III.l. $\gamma$
Expectation value (of 1-density)      V.B. $\alpha$
Face map      III.A. $\alpha$
Factor      V.I
Factors of type       $III_{\lambda}$ .V.5
Faithful representation      V.I
Faithful weight      V.3
Fermi level      IV.6. $\gamma$
Fermion kinetic term      VI.3.b—VI.5. $\beta$
Fermion number operator      IV.9. $\beta$
Fermionic action      VI.3
Fermionic Hamiltonian      IV.9. $\beta$
Fermionic Hilbert space      IV.9. $\beta$
Fine structure constant      IV.6.0
Finite adeles      V.ll. $\gamma$
Finite difference component      VI. 5. $\delta$
Finite difference degree      VI.3.b
Finite place      V.ll. $\gamma$
Finite projection      V.I
Finite projective module      II.1
Finite rank endomorphism (of C* -module)      II.A
Finitely generated projective module      II. 1
Finitely summable (Fredholm module)      IV
Flow of weights      V.8
Foliation      1.4. $\beta$
Foliation chart      1.4. $\beta$
Folner condition      V.9
Fractals      IV. 3
Fredholm module      IV
Fredholm representation      IV
Free (action of groupoid)      II.8
Free action (of group)      II.7
Free loop space      III.2. $\gamma$
Fuchsian group of second kind      IV.3. $\varepsilon$
Full sub C* -algebra      I.A
Fundamental class in K-theory (foliation)      II.6.a
Fundamental groupoid (of a manifold)      II.4.a
G-equivariant index (G Lie group)      l.10
G-equivariant map (G smooth groupoid)      II src='/math_tex/c745b9b57c145ec5577b82542b2df54682.gif'
G-manifold (G smooth groupoid)      II.10. $\alpha$
Generalized homology      II.B
Generalized trace      V.5. $\beta$
Geometric cycle (for foliation)      II.8. $\gamma$
Geometric cycle (for group action)      II. 7
Geometric cycle (smooth groupoids)      II.10. $\alpha$
Geometric group (of group action)      H.7
Geometric realization (of simplicial space)      III.A. $\alpha$
Gluon field      VI.5. $\beta$
Godbillon-Vey class      III.6
Godbillon-Vey invariant      III.6
Golden-Thompson inequality      IV.9. $\alpha$
Graded C* -algebra      IV.A
Graded C*-module      IV.A
Graded commutator      IV.A
Graph (of foliation)      II.8
Gromov distance      VI.3.b
Group cohomology      III.1. $\alpha$
Groupoid      II. 5
Growth of algebra      IV.2. $\delta$
H-unital algebra      III.1. $\gamma$
Haagerup inequality      HI.5.K
Half-densities (von Neumann algebras)      V.B. $\alpha$
Half-exact functor      II.B
Hall conductivity      IV.6. $\beta$
Hall current      IV.6. $\beta$
Harmonic measure      IV.3. $\delta$
Hausdorff distance      VI.3.b
Hecke algebra      V.10. $\beta$ —V.ll. $\alpha$
Hecke operator      V.11
Hereditary sub-C*-algebra      II.A
Hermitian finite projective module      II.1—VI.1
Hermitian form (on finite projective module)      II. 1
Hermitian structure (on finite projective module)      II.1—VI.1
Higgs kinetic term      VI.3.b—VI.5. $\beta$
Higgs self-interaction      VI.3.b—VI.5. $\beta$
Higher index theorem (for discrete groups)      III.4. $\gamma$
Higher index theorem (for etale smooth groupoid)      III.7. $\gamma$
Higher trace      III.6. $\alpha$
Hilbert algebra      V. 3
Hilbert transform      IV.3. $\alpha$
Hochscnild cohomology      III.1. $\alpha$
Holonomy (for a foliation)      1.4. $\gamma$
Holonomy groupoid (of foliation)      II.8. $\alpha$
Homotopic asymptotic morphisms      II.B
Homotopic Kasparov bimodules      IV.A
Homotopy invariance of cyclic cohomology      Ill.l. $\gamma$
Homotopy of *-homomorphisms      II.A
Homotopy quotient (for compact group      Vl.2. $\gamma$
Homotopy quotient (for discrete group)      II. 7
Hopf algebra      IV.8. $\beta$
Horizontal distribution (for foliation)      lll.7. $\alpha$
Horocycle foliation      II.9. $\gamma$
Hyperbolic group      III.5. $\gamma$
Hyperbolic metric space      III.5. $\alpha$
Hypercharge      VI.5. $\beta$ —VI.5. $\varepsilon$
Hyperfinite factor      V.1—V.6
Hyperfinite von Neumann algebra      V.6
Hypertrace      V.9. $\alpha$
Idele class group      V.11. $\gamma$
Identity correspondence      V.B. $\alpha$
Index groupoid (of linear map)      II.6. $\varepsilon$
Index of sub factor      V.10. $\alpha$
Index theorem for measured foliations      1.5. $\gamma$
Induced automorphism      V.8. $\alpha$
Induced Kasparov bimodule      IV.A
Infinite-dimensional cycle      IV.7. $\beta$
Injective von Neumann algebra      V.7. $\beta$
Inner automorphism (of C* -algebra)      II.C
Integrable subbundle      1.4. $\beta$
Integrable weight      V.8. $\gamma$
Integral logarithm      IV.8. $\alpha$
Integrality of pairing      IV.l. $\gamma$
Interpolation ideals      IV.2. $\varepsilon$
Interpolation square      IV.2. $\varepsilon$ —IV.B
Intersection product      IV.A
Invariant transverse density      I.4
Irrational rotation C*-algebra      II.8. $\beta$
Isomorphic measured equivalence relations      V.4
Isotypic representation      V.1. $\gamma$
ITPFI      V.4
J.L.O. cocycle      IV.8. $\varepsilon$
K-cycle      IV.2. $\gamma$
K-orientation      II.6. $\gamma$
K-theory      II. 1
K-theory (algebraic)      III. 3
K.M.S. condition      I.2
Kasparov bimodule      IV.A
Kasparov bivariant theory      IV.A
Kasparov product      IV.A
Klein — Gordon equations      IV.9. $\beta$
Kobayashi — Maskawa mixing matrix      VI.5. $\gamma$
Koebe 1/4 theorem      IV.3. $\beta$
Kolmogorov — Sinai theorem      V.6. $\beta$
Krieger factors      V.4
Kronecker foliation      1.4. $\beta$
Kubo formula      IV.6. $\gamma$
Laplace transform      IV.8. $\beta$
Lattice      V.11. $\gamma$
Leaf (of foliation)      1.4. $\beta$
Left Hilbert algebra      V.3
Lipschitz function      VI.1
Local observables      IV.9. $\beta$
Local triviality (of foliation)      1.4. $\beta$
Locally compact field      V.11. $\gamma$
Locally convex algebra      III.B

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