Phillips N.Ch. — Equivariant K-Theory and Freeness of Group Actions on C*-Algebras :: Электронная библиотека попечительского совета мехмата МГУ

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Phillips N.Ch. — Equivariant K-Theory and Freeness of Group Actions on C*-Algebras

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Название: Equivariant K-Theory and Freeness of Group Actions on C*-Algebras

Автор: Phillips N.Ch.

Аннотация:

This book is based on the author's Ph.D. thesis written at the University of California at Berkeley. However, it incorporates substantial revisions and many additional results. The research reported here has been partially supported by a National Science Foundation Graduate Fellowship, by the Mathematical Sciences Research Institute (NSF Grant 8120790). and by a National Science Foundation Postdoctoral Fellowship. All of this support is gratefully acknowledged. Thanks are also due to Marsha Colby, who converted an enormous number of sometimes rather illegible handwritten pages into the computer files from which this manuscript was produced, and who, with rare exceptions, was able to persuade a University of California computer to print many symbols that it had never been intended to make.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1987

Количество страниц: 371

Добавлена в каталог: 17.04.2008

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Предметный указатель

Induction in stages      168 172 176
Inner action      44
Inner automorphism      45
Inner derivation      91 98
Inner product      24—27 42—43 111 117 238—241 293
Integrated form of a representation      17 38—39 43 51—52 135 198 238 241 283
Invariant subquotient      251 254 256—261 274 279—282
Inverse limit of groups      156 325—328
Inverse limit of spaces      144
Invertible element of $KK_{G}(A,B)$       107
Irrational rotation algebra      263—265
Irreducible representation of C*-algebra      280 283
Irreducible representation of group      19 41 47 65
Isomorphism of prequasihomomorphisms      73
Julg's Theorem      3 12 33 38 44 49—51 59 197 241
Julg, P.      2 3 12 16 17 18 20 36 38 167
K (= $K(L^{2}(G)\otimes l^{2})$ )      70
K(E) (compact module morphisms)      117
K(H) (compact operators)      46
K-amenability      211
K-freeness      2—5 131 136—151 153 155 164—165 179—181 189 211—213 234—236 242 258—265 270 272—275 281—294 290—305 309
K-freeness and actions with K-free restrictions      143 167 179 181 299—302
K-freeness and AF actions      5 286—292 302—305 see
K-freeness and bundles of C*-algebras      146
K-freeness and commutative algebras      138
K-freeness and composition series      141—142
K-freeness and crossed products by $F_{n}$       213
K-freeness and crossed products by R      213
K-freeness and crossed products by Z      211—212
K-freeness and direct limits      141
K-freeness and extensions      137
K-freeness and exterior equivalent actions      139 141 212
K-freeness and free action on the primitive ideal space      281
K-freeness and hereditary saturation      236 251 258—259 263 300
K-freeness and hereditary subalgebras      141 142
K-freeness and ideals      137 287
K-freeness and K-theory of the fixed point algebra      270 272—273
K-freeness and KK-freeness      153 155
K-freeness and locally representable actions      294 298
K-freeness and product type actions      293—294 298—302 309
K-freeness and quotients      137
K-freeness and restrictions of actions to subgroups      137—138 167 282 294 302—305
K-freeness and stably isomorphic G-algebras      140
K-freeness and strong Connes spectrum      236 251 258—259 263 300
K-freeness and tensor products      140 143 144—145 229 234—235
K-freeness and total K-freeness      137—138 234 302—305
K-freeness and twisted products      146
K-freeness and type I algebras      5 275 281—285
K-freeness up to torsion      178—179 181
K-freeness, total      see "Total K-freeness"
K-saturation      270—274 285
K-saturation, hereditary      270—274 281 285 299
K-saturation, hereditary up to 2-torsion      272
K-theory of $L^{1}(G,A,\alpha)$       38
K-theory of crossed products      38—44 53 210—211 see
K-theory of crossed products, R(G)-module structure on      48—51
K-theory of fixed point algebra      4 240—242 250 270—274 285 see
K-theory, action on, induced by dual action      50—51
K-theory, discrete      see "Discrete K-theory"
K-theory, equivariant      see "Equivariant K-theory"
K-theory, locally discrete      see "Locally discrete K-theory"
K-theory, order on      252 294—295 297 305
K-theory, positive element in      244—295 297
K-theory, totally positive element in      251—252 256—257 259—260 266—269 294
K-visibility      236—237 251—252 261 265—270
K-visibility, high      236 251—253 256—257 259 261 264—270 272 285
K-visibility, p-weak      251 256—258 263 266—270 272 274
K-visibility, weak      273
Kaplansky, I.      31
Kasparov group (temporarily denoted $\overline{KK}_{G}(A,B)$ )      121—124 see
Kasparov product      68 81 90—91 95—105 106—109 114—116 129 152 159—161 171—177 309 321 327
Kasparov, G.G.      2 3 58 64 68 69 104 105 109 117 120 124 125 171 173 325
Keimel, K.      76 146 157 158
Kelley, J.L.      162
Kishimoto, A.      4 212 213 228 236 246 249 250 261 263 283 284 300
KK-freeness      3—5 131 151—157 161—162 164—165 167 181 162 185 190 233—234 278—279 286 307—308 326
KK-freeness and actions with KK-free restrictions      167 181
KK-freeness and AF algebras      5 286 307 306 see
KK-freeness and C(X)-algebras      131 161
KK-freeness and commutative algebras      156—157 161
KK-freeness and composition series      157 279
KK-freeness and extensions      154
KK-freeness and free action on the primitive ideal space      3 157 279
KK-freeness and ideals      154
KK-freeness and K-freeness      153 155
KK-freeness and locally representable actions      328
KK-freeness and quotients      154
KK-freeness and restrictions of actions to subgroups      4 167 165 233 307
KK-freeness and stably isomorphic algebras      155
KK-freeness and tensor products      154—155 233
KK-freeness and total K-freeness      157
KK-freeness and type I algebras      278—279
KK-freeness, total      152
KK-Subgroup Theorem      185 233 307
KK-theory, discrete      see "Discrete KK-theory"
KK-theory, equivariant      see "Equivariant KK-theory"
KK-theory, locally discrete      152
Kleinecke — Shirokov theorem      165
Kuenneth formula, equivariant localized      4 67 189—190 200 215 218—221 229—233 235
Kuenneth formula, in ordinary K-theory      144 189 201—202 209 267—268
L(E) (adjointable module homomorphisms)      117
L(E) (bounded operators)      16
L(H) (bounded operators)      46
L(v)      28
L(V,W)      28
Lance, E.G.      128 129 139 140 283 284
Lang, S.      200 216
Laurent polynomial ring      156—157 302
Left regular representation      39 60 65 70 133 164 172 213 258 259 261 264 283 292—298 302 306 316
Lifting of derivation      72 85 87 93 95
Limit, inverse      144 156 325—328
Line bundle      110 156
Local ring      216
localization      6
Localization of an algebra over a ring      152
Localization theorem      6 10 139 149 151 163 200
Localized equivariant Kuenneth theorem      4 67 189—190 200 215 218—221 229—233 235
Locally closed set      253—258 268
Locally contractible space      189
Locally convex C(X)-module      158
Locally discrete K-theory      131—138 141—146 157 178 185 211 224 232 235 271 286—296 299 328
Locally discrete K-theory and AF actions      286—296 299 328
Locally discrete K-theory and commutative algebras      132 134
Locally discrete K-theory and crossed products by $F_{n}$ , R and Z      211
Locally discrete K-theory and direct limits      141
Locally discrete K-theory and discrete K-theory      157
Locally discrete K-theory and extensions      133
Locally discrete K-theory and ideals      133—136 287—289
Locally discrete K-theory and K-theory of fixed point algebra      271
Locally discrete K-theory and locally representable actions      294 296 328
Locally discrete K-theory and product type actions      293 299
Locally discrete K-theory and quotients      133 287—289
Locally discrete K-theory and restriction of actions      178 182 294
Locally discrete K-theory and twisted products      146
Locally discrete K-theory and type I algebras      134—136
Locally discrete KK-theory      152
Locally representable action      5 286 292—299 305 309 327—328
Locally representable action and discrete KK-theory      328
Locally representable action and equivariant KK-theory      327
Locally representable action and K-freeness      294 298
Locally representable action and KK-freeness      328
Locally representable action and locally discrete K-theory      294 296 328
Locally representable action and total K-freeness      294—295
Locally representable, action which is not      305
Locally trivial continuous field      208
M(A) (multiplier algebra)      44
M(G) (measure algebra)      21
MacDonald, I.G.      6 8 9 10 141 144 152 179 196 216 296 326
Mapping cone      61 217—218
Matsumura, H.      215 216

Maximal ideal in C*-algebra      24
Maximal ideal in ring      216
Maximal ideal space      3 162 163 309
Maximal tensor product      159 234
Mayer — Vietoris sequence      67
Measure algebra      21
Metric, hermitian (on vector bundle)      24—27 111
Milnor $\lim\limits_{\longleftarrow}^{}^{1}$ -sequence      156 325
Mingo, J.A.      117
Minimal ideal      19 310 324
Minimal idempotent      39—40
Minimal invariant ideal      290 292 310 327
Minimal polynomial      200—201 230
Minimal projection      311 313
Minimal tensor product      104 191
Miscenko, A.S.      58 125
Module structure on $K_{*}(C^{*}(G,A))$       48—51
Module, (G,A, $\alpha$ )-      16 see finitely over
Module, (partially) ordered      294 297 298 305
Module, (projective) resolution of      215 217 220
Module, C(X)-      157 158
Module, finitely generated projective over a C*-algebra      12 15 16—30 39 41 45 47 50 132—133 167—170 197—198 238 241
Module, flat      204
Module, free, over a C*-algebra      16 17 197 298
Module, graded      191
Module, Hilbert      117—127
Module, locally convex C(X)-      158
Module, pre-Hilbert      42
Module, projective, over a C*-algebra      12 15 16—30 39 41 45 47 50 132—133 167—170 197—198 238 241
Module, projective, over a ring      16 190 200—208 214—221 229 232
Moore, C.C.      280
Morita equivalence bimodule      236—240
Morita equivalence of fixed point algebra and crossed product      4 236—239 243 285 298
Morita equivalence, strong      4 66 236—239 243—244 285 298
Multiplicative system      6 152 272 293
Multiplicity of a representation      60 71 133 299
Multiplier      39 41 44 63 69
Multiplier algebra      44—46 55 63 68—70 75 80 117 118 122 124—127 134 136 139 158—159 198 207 239 242 245 277 284 322 see
Multiplier algebra, G-      68 69—74 81—86 90—101 105—107 119—120 124 158 325
Murray — von Neumann equivalence      28—33 41—42
Murray — von Neumann equivalence, in C*-algebraic sense      31—33 46—47 127
N (category related to Kuenneth formula)      201
Normal representation      203
Nuclear C*-algebra      4 124 139—140 149—154 167 184 185 190 196—234 267 268 270 325
O(E) (sheaf)      114
Olesen, D.      4 137 212 236 252 255
One point compactification      14
One-cocycle      44 46 139 198 311
Operator, compact, on Hilbert module      117
Operator, degree of      121
Operator, differential      112
Operator, elliptic      58 68 109 112 167 179
Operator, Fredholm, on Hilbert module      125—127
Operator, Fredholm, on Hilbert space      112—113 115
Operator, grading      121 122
Operator, index of      112 125
Operator, order of      112
Operator, preudodifferential      111—112 114—115
Operator, symbol of      112 115
Order of operator      112
Ordered group      252 294 297 298
Ordered R(G)-module      294 297 298 305
Outer action      298 305
Outer automorphism      236
p-group      4 143 167 179—181 190 230—234 288—289
p-weakly K-visible C*-algebra      251 256—258 263 266—270 272 274
p.q.h. (=prequasihomomorphism)      75 see
Pairing in equivariant K-theory      191—200
Palais, R.      111 112 114
Partially ordered group      252 294 297 298
Partially ordered R(G)-module      294 297 298 305
Paschke, W.L.      42 43 63 117 236 237 239 240
Pedersen, g.k.      4 15 17 39 41 44 50 51 52 60 62 63 70 72 81 85 94 120 122 137 138 139 140 141 149 164 198 207 209 212 213 236 238 246 249 250 252 255 264 278 283 300 316
Petrie, T.      190
Phillips, N.C.      5
Phillips, W.J.      117
Pimsner — Voiculescu exact sequence      190 209 210 214
Pimsner, M.      190 209 210
Polynomial ring      8 156—157 200—201 230 302
Polynomial ring, Laurent      156—157 302
Polynomial, minimal      200—201 230
Positive element of $K_{0}(A)$ or $K^{G}_{0}(A)$       294—295 297 see
Positive functional      42—43 237—238
Pre-Hilbert module      42
Prequasihomomorphism      68 73—91 95—106 111—115 119—120 124—129 160—161 171—174 321
Prequasihomomorphism, defined by an equivariant homomorphism      78
Prequasihomomorphism, direct sum of      78
Prequasihomomorphism, equivariant      73
Prequasihomomorphism, extended      see "Next entry"
Prequasihomomorphism, extendible      81—85 87—90 93 95—100 105
Prequasihomomorphism, extension of      see "Previous entry"
Prequasihomomorphism, G-homotopy of      76
Prequasihomomorphism, homotopy of      76
Prequasihomomorphism, isomorphism of      73
Prequasihomomorphism, quasihomomorphism defined by      74—75
Prequasihomomorphism, split      99—100 102—103
Prim(A) (primitive ideal space)      139
Prime ideal      6
Prime ideal in R(G), support of      10 139 149—151 163 179 189 200 213 215—221 229 231 232 281
Primitive ideal space      3 5 131 139—140 145 149—151 203 206—208 212 219 221 222 224—227 250 252—259 266 268—269 275—285 291 299 300
Primitive ideal space, free action on      3 5 131 151 221—222 227 275 278—282 283 299
Primitive ideal space, separated point in      149
Primitive ideal space, topology on      139—140 149
Primitive root of unity      200 216 230 260 299 302
Product type action      286 292—294 298—302 305 309
Product type action, equivariant K-theory of      293
Product type action, hereditary saturation of      301
Product type action, K-freeness of      293—294 298—302 309
Product type action, locally discrete K-theory and      293 298
Product type action, total K-freeness of      299
Product, inner      24—27 42—43 111 117 238—241 293
Product, Kasparov      68 81 90—91 95—105 106—109 114—116 129 152 159—161 171—177 309 321 327
Projection (=selfadjoint idempotent)      18
Projection, minimal      311 313
Projections, equivariant K-theory in terms of      31—33
Projective $(G,A,\alpha)$ -module      16 see
Projective dimension      215
Projective module over a C*-algebra, finitely generated      12 15 16—30 39 41 45 47 50 132—133 167—170 197—198 238 241
Projective module over a ring      16 190 200—208 214—221 229 232
Projective representation      40 138 140 154 232 280 289
Projective resolution      215 217 220
Projective space      110 156
Projective unitary representation      48 138 140 154 232 280 289
Proper map      13—15 55
Pseudodifferential operator      111—112 114—115
Pseudodifferential operator, symbol of      112 115
Pullback      2 6 14 67 129
q.h. (=quasihomomorphism)      75 see
Quasicentral approximate identity      81 84 87—89 93
Quasihomomorphism      68 73—90 96—98 102—105 109 119—120 160—161 321
Quasihomomorphism, defined by a prequasihomomorphism      74—75
Quasihomomorphism, direct sum of      78
Quasihomomorphism, extended      see "Quasihomomorphism extendible"
Quasihomomorphism, extended, defined by an extended prequasihomomorphism      82
Quasihomomorphism, extendible      68 81—86 89 90 102—103
Quasihomomorphism, extension of      see "Previous entry"
Quasihomomorphism, G-homotopy of      75
Quasihomomorphism, homotopy of      75
Quasinilpotent      165
R (= $R(G)_{P}$ )      200
R(G) (representation ring)      14
Radical      9 144 178—179
Rectangular ideal      224—226 231 233
Reduced crossed product by $F_{n}$       210—211 213—215 219 221
Reduced crossed product by locally compact group      209
Reduced group C*-algebra of $F_{n}$       229
Regular local ring      216
Regular representation of $L^{1}(G,A,\alpha)$       209
Regular representation of group      39 60 65 70 133 164 172 213 258 259 261 264 283 292—290 302 306 316
Representation of C*-algebra      42—43 51—52 112 121 123 149 209 278 280—281 283

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