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Le Bruyn L. — Noncommutative geometry
Le Bruyn L. — Noncommutative geometry

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Название: Noncommutative geometry

Автор: Le Bruyn L.

Аннотация:

Noncommutative geometry is the study of families of (commutative) algebraic
varieties (with specified connecting morphisms) which are locally controlled
by noncommutative algebras.


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 355

Добавлена в каталог: 14.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$GL_n$ variety      42
Abelian category      84
Abelianization      252
Action, contragradient      14
Action, free      156
Action, locally finite      56
Acyclic object      84
Acyclic resolution      84
Additive category of quiver      256
Adelic Grassmannian      336
Adjoint matrix      72
Admissible vertex      313
Affine scheme      81
alg $@_n$      36
alg$^t$      35
Algbera, quantum enveloping      199
Algebra, $A_{\infty}$      289
Algebra, algebraic functions      83
Algebra, associated graded      124 252
Algebra, Azumaya      86 120
Algebra, center      35
Algebra, connected graded      20
Algebra, deformed preprojective      193
Algebra, differential graded      278
Algebra, differentially graded      145
Algebra, dual numbers      123
Algebra, extension      146
Algebra, formal necklace      25
Algebra, formal trace      25
Algebra, free product      269 282
Algebra, free trace-      35
Algebra, group      272
Algebra, Henselian      83
Algebra, Hopf      200
Algebra, infinite necklace      26
Algebra, infinite trace      26
Algebra, infinitesimal extension      132
Algebra, local      124 146
Algebra, marked quiver-necklace      141
Algebra, n-th root      254
Algebra, necklace      19
Algebra, path      91
Algebra, Poisson      252 297
Algebra, preprojective      193
Algebra, pull-back      133
Algebra, quaternion      325
Algebra, Quillen smooth      91
Algebra, quiver trace      98
Algebra, Rees      253
Algebra, semisimple      16
Algebra, strict Henselian      83
Algebra, super      281
Algebra, variety      202
Algebra, Weyl      252 337
Algebra, Weyl-      42
Algebra, with trace      35
Algebra, witness      62
Algebraic group      201
Algebraic quotient      58
Analytic topology      81
Artin — Mumford exact sequence      116
Artin, M.      77 120 205
Associated graded algebra      124 252
Associated quiver setting      222
Associativity constraint      251
Atiyah class      253
Azumaya algebra      86 120
Azumaya locus      142
Balanced coweight      208
Barcode      310
Based linear map      279
Berest, Y.      339 340
Bernstein filtration      339
Berstein — Gelfand — Ponomarev reflection functor      153
Bimodule      292
Bipartite double      161
Birkes, D.      77
Bockland, R.      205 302 340
Border      222 232
Border of corner      222
Borel subgroup      224
Boundary      95
Bracker invariant      258
Brauer group      89
Calogero system      329
Cannings, R.      337 340
Canonical decomposition      148 172
Canonical right ideal      338
Canonical, $A_{\infty}$-structure      289
Capacity      119
Cartan decomposition      55
Cartan homotopy formula      297
Cartan matrix      199
Cartan, matrix      147
Category, abelian      84
Cayley — Hamilton algebra      35
Cayley — Hamilton formal polynomial      29 35
Cayley — Hamilton theorem      29
Cayley-smooth locus      172
Cayley-smooth model      188 189
Cayley-smooth, $\alpha$-      194
Center of algebra      35
CHARACTER      216 266 304
Characteristic polynomial      3 29
Chern numbers      271
Chevalley theorem      148
Chevalley, theorem of      44
Chinese remainder theorem      87
Closed form      281
Cobracker invariant      258
Cohomology, dimension      110
Cohomology, etale      85
Cohomology, Galois      88
Cohomology, pointed set      85
Commutator element      193 312
Commutator filtration      252
Compact subgroup      303
Compartment      160
Completion, lifting algebra      284
Complex moment map      193
Composition factors      53
Composition factors, multiplicities      53
Composition series      53
Cone, tangent      124
Coniveau spectral sequence      114
Connecting morphism      269
Connecting sum map      271
Connection      286
Constant sheaf      82
Constructible set      45
Continuous module      88
Contraction operator      289
Coordinate map      20
Coregular quiver spaces      202
Corner      210 232
Corner type      232
Corner, border      222
Corner, optimal      221
Cotangent bundle      193
Covector      14
covers      81
Crawley-Boevey, W.      162 205 340
Cuntz, J.      302
Curvature      279
Cycles      95
Cyclic vector      312
Deformed preprojective algebra      193
deRham cohomology groups      278
deRham cohomology, big      288
deRham cohomology, big relative      293
deRham cohomology, noncommutative      288 291
deRham cohomology, noncommutative relative      294
deRham complex      278
Derivation point      125
Derivation trace preserving      124
Derivation with respect to morphism      124
Derived functor      84
Derived functor, right      84
Derksen, H.      163 302
Differential      126
Differential form, noncommutative      278
Differential form, relative      292
Differential graded      278
Differential operator, exterior      277
Differentially graded algebra      145
Dimension formula      127
Dimension vector      60 64 93
Dimension vector, minimal      333
Dimension vector, sincere      147
Dimension vector, support      102
Dimension, local      125
Direct image      108
Direct order      237
Discriminant      8
Divisor, ramification      120
Dominance order      64 65
Dominant weight      207
Domokos, M.      302
Double centralizer theorem      16
Double quiver      312
Dual numbers      123
Dual partition      23
Dynkin diagram      147
Equalizer diagram      82
Equivalent marked quiver      180
Equivariant map      19
Etale cohomology functor      85
Etale locally split      185
Etale morphism      81
Etale neighborhood      83
Etale presheaf      82
Etale sheaf      82
Etale site      81
Etale stalk      84
Etale topology      81
Euler derivation      289
Euler form      95
Evaluation map      15
Extension      94
Extension algebra      146
Exterior product      277
Fedosov product      280
Field Tate      110
Field Tsen      109
Filtration, adic      124
Filtration, finite      50
Fixed elements      154
Flag variety      224
Formal $A_{\infty}$-algebra      289
Formal Cayley — Hamilton polynomial      29 35
Formal completion      253 255 256
Formal necklace algebra      25
Formal structure      251—253 267
Formal structure sheaf      256
Formal substitution      32
Formal trace algebra      25
Formal trace map      25
Formanek, E.      39
Free action      156
Free product      269
Free product algebra      282
Free product, algebra      273
Free product, group      272
Function, algebraic      83
Function, elementary symmetric      5
Function, Morse      75
Function, polynomial      6
Function, special      74
Functor, derived      84
Fundamental group      271
Fundamental set of roots      149
Gabriel, P.      162
Galois absolute -group      87
Galois cohomology      88
General subrepresentation      211
Generic representation      149
Generic semi-simple type      172
Gerstenhaber      67
Ginzburg, V.      302 340
Global section      82
Going-down propoerty      46
Good vertex      103
Graded localization      216
Grassmann variety      311
Grassmannian, adelic      336
Grothendieck topology      81
Grothendieck topology, noncommutative      254
Group algebra      272
Group, Brauer      89
Group, cohomological dimension      110
Group, multiplicative      83
Group, reductive      54
Group, unitary      54 72
Gurevich, G.B.      39
Haar measure      54
Hamilton equations      329
Hamiltonian action      334
Hamiltonian flow      335
Happel, D.      163
Hazewinkel, M.      77
Henselian algebra      83
Henselian, strict      83
Henselization, strict      83
Hermitian inproduct      303
Hermitian skew -matrices      72
Hermitian transpose      54
Hermitian, inproduct      72
Hesselink stratification      225
Hesselink stratum      225
Hesselink, W.      67 225 247
Hilbert criterium      48 49
Hilbert scheme      320
Hilbert theorem      90 89
Hilbert — Chow map      325
Hochschild — Serre spectral sequence      111
Holland, M.      205 337 340
Homology groups      143
Hopf algebra      200
Hulek, K.      271
Ideal of relations      41
Ideal, maximal      81
Ideal, prime      81
Ideal, trace relations      37
Idempotent      23
Implicit function      81
Implicit function theorem      46
Indecomposable projective      265
Indecomposable representation      146
Indecomposable roots      147
Index, ramification      119
Inertia      119
Inertial degree      119
Infinitesimal extension of algebra      132
Infinitesimal extension, trivial      132
Infinitesimal extension, versal      133
Injective object      84
Injective resolution      84 145
Integrable system      329
Integral extension      44
Invariant polynomial      10 56
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