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

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

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

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

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.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 371

Добавлена в каталог: 17.04.2008

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

Предметный указатель

$(G,C_{0}(X))$ -algebra 158—159 162—164 219 248 277 278
$(Z/2Z)^{2}$ see "Action of $(Z/2Z)^{2}$ "
$(Z/2Z)^{2}\times Z/3Z$ see "Action of $(Z/2Z)^{2}\times Z/3Z$ "
$(Z/2Z)^{3}$ see "Action of $(Z/2Z)^{3}$ "
$(\varphi/\psi)_{*}$ (difference map in K-theory) 128
$(^{n}_{j})$ (binomial coefficient) 258
$a\oplus b$ (direct sum of matrices) 28
$A\oplus_{max}B$ (maximal tensor product) 159
$A\otimes B$ (minimal tensor product) 104
$A^{+}$ (unitization) 22
$A^{G}$ (fixed point algebra) 58
$A_{\tau}$ (eigenspace for action) 137
$A_{\vartheta}$ (rotation algebra) 263
$C(G\times_{H}A)$ (twisted product) 64
$CP^{n}$ (projective space) 156
$C^{*}_{r}(G)$ (reduced group C*-algebra) see " $$C^{*}_{r}(G</a> <a href=$
$C^{*}_{r}(G,A)$ (reduced crossed product) see " $$C^{*}_{r}(G</a> <a href=$
$C^{*}_{r}(G,A,\alpha)$ (reduced crossed product) 209
$C_{0}(X)$ (continuous functions vanishing at $\infty$ ) 22
$C_{0}(X)$ -algebra 157—159 162—164 219 248 277 278
$C_{0}(X,A)$ (continuous A-valued functions vanishing at $\infty$ ) 17
$C_{b}(X)$ (bounded continuous functions) 277
$C_{c}(X)$ (compactly supported continuous functions) see " $$C_{c}(X</a> <a href=$
$C_{c}(X,A)$ (compactly supported continuous A -valued functions) 17
$C_{\varphi}$ (mapping cone) 61
$d_{A}$ 174
$d_{G,H,A}$ 174
$D_{\Phi}$ (map associated to a p.q.h.) 73
$Ext_{G}(A,B)$ (equivariant extensions) 125
$E\oplus F$ (Whitney sum) 13
$E\otimes F$ (tensor product of bundles) 13
$E\otimes_{A}B$ (tensor product of module and algebra) 17
$E_{x}$ (fiber of vector bundle) 13
$f^{+}$ (map of one point compactifications) 14
$F_{n}$ (free group) 210
$G\times_{H}X$ (twisted product) 64
$G_{x}$ (stabilizer subgroup) 7
$Hom_{f}(E,F)$ (set of vector bundle maps) 22
$Hom_{g}(E,F)$ (set of maps of vector bundles of modules) 22 23
$Hom_{\varphi}(E,F)$ (set of module maps) 23
$H^{m}$ (sheaf cohomology) 114
$H^{s}$ (Sobolev space) 111
$H^{\infty}_{B}$ 117
$h_{*}$ (= $K^{G}_{*}(\cdot)_{P}$ ) 200
$h_{*}$ (equivariant homology theory) 184
$H_{B}$ (Hilbert space over B) 117
$Ind^{G}_{H}$ (induction map in K-theory) 168
$Ind^{G}_{H}$ (induction map in KK-theory) 174
$Ind^{G}_{H}$ (induction of modules) 187
$I^{-}_{S}$ (from ideal Decomposition Lemma) 183
$I^{G}_{H}$ (induction map in KK-theory) 171
$I^{G}_{H}$ (map in KK-theory) 171—177 321—323
$I_{A}$ 174
$i_{G,H,A}$ 174
$I_{S}$ (from ideal Decomposition Lemma) 183
$K(E_{1},E_{2})$ (compact module morphisms) 117
$KK^{*}_{G}(A,B)$ (equivariant KK-theory) 116
$KK^{0}_{G}(A,B)$ (equivariant KK-theory) 116
$KK^{1}_{G}(A,B)$ (equivariant KK-theory) 116
$KK_{G}(A,B)$ (equivariant KK-theory) 78
$K^{*}_{G}(X)$ (equivariant K-theory) 1
$K^{0}_{G}(X)$ (equivariant K-theory) 13 14
$K^{1}_{G}(X)$ (equivariant K-theory) 15
$K^{G}$ -visibility 261
$K^{G}_{*}(A)$ (equivariant K-theory) 51
$K^{G}_{0}(A)$ (equivariant K-theory) 17 22
$K^{G}_{1}(A)$ (equivariant K-theory) 51
$L(E_{1},E_{2})$ (adjointable module homomorphisms) 117
$L(V,W)\otimes A$ 28
$L^{1}(G,A)$ (twisted $L^{1}$ -algebra) see " $$L^{1}(G</a> <a href=$
$L^{1}(G,A,\alpha)$ (twisted $L^{1}$ -algebra) 18
$M_{G}(A)$ (G-multiplier algebra) 69
$M_{n}$ ( $n\times n$ complex matrices) 39
$M_{P}$ (localization of module) 6
$N^{G}$ (category related to Tensor Product Theorem) 221
$N^{G}_{0}$ (category related to equivariant localized Kuenneth formula) 215
$N^{G}_{1}$ (category related to equivariant located Kuenneth formula) 221
$N^{G}_{nuc}$ (category related to Tensor Product Theorem) 229
$O_{n}$ (Cuntz algebra) 241
$Proj_{G}(A)$ (finitely generated projective $(G,A,\alpha)$ -modules) 23
$p\oplus q$ (direct sum of idempotents) 28
$P_{(as\ subscript)}$ (localization) 6
$P_{G}(A)$ (set of G-invariant idempotents) 28
$Q_{\Phi}$ (map associated to a p.q.h.) 73
$Res^{G}_{H}$ (restriction map in K-theory) 168
$Res^{G}_{H}$ (restriction map in KK-theory) 171
$Res^{G}_{H}$ (restriction of modules) 167
$R_{+}(G)$ (positive part of R(G)) 58
$R_{P}$ (localization of ring) 6
$S^{1}$ see "Circle group"
$S^{1}$ (circle group) 19
$S^{1}$ (circle) 6
$S^{2}A$ (second suspension) 116
$S^{—1}M$ (localization of module) 6
$S^{—1}R$ (localization of ring) 6
$S_{G}(A)$ (semigroup of idempotents) 28
$U^{G}(V,A)$ (G-invariant unitaries in $L(V)\otimes A$ ) 58
$U^{G}_{0}(V,A)$ (identity component of $U^{G}(V,A)$ ) 58
$Vect_{G}(X)$ (G-vector bundles) 23
$X^{+}$ (one point compactification) 14
$Z/2Z\times Z/2Z$ see "Crossed product by $Z/2Z\times Z/2Z$ "
$[\Phi]$ (class of q.h. or p.q.h. in KK-theory) 78
$[\Phi][\Psi]$ (product of classes of (pre-)quasihomomorphisms) 90
$[\varphi]$ (class of homomorphism in KK-theory) 80
$\alpha^{+}$ (action on unitization) 22
$\alpha_{(\cdot)}|_{I}$ (restriction of action to invariant subset) 136
$\Box$ (operator on differential forms) 112
$\eta\otimes_{D}\lambda$ (product in KK-theory) 104
$\eta_{*}$ (map in KK-theory) 60
$\Gamma(E)$ (sections of vector bundle) 23
$\Gamma(\alpha)$ (Connes Spectrum) 249
$\Gamma^{\infty}(E)$ ( $C^{\infty}$ sections of vector bundle) 111
$\Gamma_{0}(A)$ (sections vanishing at infinity) 146
$\lambda\Phi$ (prequasihomomorphism) 73
$\lambda\Phi$ (quasihomomorphism) 75
$\lambda^{*}$ (map in KK-theory) 80
$\Lambda^{i}$ (exterior power) 110
$\lim\limits_{\longleftarrow}^{}^{1}$ 156 325—326
$\lim\limits_{\longrightarrow}$ (direct limit) 33
$\omega$ (pairing in K-theory) 191
$\omega(A,B)$ (pairing in K-theory) 192
$\omega_{P}$ (pairing in localized K-theory) 196
$\omega_{P}(A,B)$ (pairing in localized K-theory) 200
$\oplus$ (direct sum) see " $a\oplus b$ " " " "
$\otimes$ (tensor product) see " $A\otimes B$ " " " " " A$"/>" "
$\overline{KK}_{G}(A,B)$ (equivariant KK-theory) 121
$\overline{U}^{G}(V,A)$ (= $U^{G}(V,A)/U^{G}_{0}(V,A)$ ) 58
$\overline{\partial}, \overline{\partial}^{*}$ (operators on differential forms) 112
$\Phi_{1}\oplus \Phi_{2}$ (direct sum of q.h. and p.q.h.) 78
$\Phi_{\eta}$ (prequasihomomorphism) 73
$\Phi_{\eta}$ (quasihomomorphism) 75
$\pi_{A}$ 174
$\pi_{G,H,A}$ 174
$\tau_{D}$ (map in KK-theory) 104
$\varphi^{A}_{\tau}$ 306
$\varphi_{*}$ (map in K-theory) 21
$\widehat{ }$ (dual group, action) see " $\widehat{G}$ " "
$\widehat{G}$ (dual group) 50
$\widehat{\alpha}$ (dual action) 50
$\widetilde{ }$ see " $\widetilde{V}$ " "
$\widetilde{Sp}(\alpha)$ (strong spectrum) 249
$\widetilde{V}$ (complex conjugate space) 39
$\widetilde{x}$ (element of C*(G,A, $\alpha$ ) gotten from $x\in A$ ) 238
$\widetilde{\Gamma}(\alpha)$ (strong Connes spectrum) 249
$\|$ $\|_{1}$ ( $L^{1}$ -norm) 18
$\|$ $\|_{2}$ (Hilbert module norm) 42
$\|$ $\|_{\infty}$ (supremum norm) 43
(ab)(g) (twisted convolution) 17
(G,A, $\alpha$ )-module 16 see
(G,C(X))-algebra 159—162 279

* (adjoint)      see "a*(g)" "
* (subscript or superscript for induced map)      see "f*(E)" "f*([E])" " " " "
* (unspecified index in (co-)homology theory)      see " $h_{*}$ " " " "
*-homomorphism      15
*-strong operator topology      71—72 118
+ (superscript for compactification or unitization)      see " $A^{+}$ " " " "
a*(g) (adjoint in $L^{1}$ algebra)      18
action      13 15
Action of $(Z/2Z)^{2}$       137—138 155 282 302 309
Action of $(Z/2Z)^{2}\times Z/3Z$       181
Action of $(Z/2Z)^{3}$       235
Action of $F_{n}$       209—211 213—215 219 281
Action of $S^{1}$       133 156 165 190 228 263—265 274 275 280—283 265 301—302 309
Action of R      201 209—211 213—214 219 227—228
Action of Z      190 201 209—214 219 227—228 263—265 283—284 290
Action of Z/2Z      4 5 134—136 143 224 251 271—274 286 299 300 302—305
Action of Z/3Z      261—263
Action of Z/4Z      5 299 302—305 309
Action of Z/6Z      299—300
Action of Z/nZ      4 5 140 143 167 177—181 189 200—209 213—222 227 229 232 264—265 271 274 275 279—282 285 288 299 302 305 307—308
Action of Z/pZ (p prime)      189 229 258 270 273 299
Action on a Banach algebra      15
Action on a C*-algebra      15
Action on a crossed product C*-algebra      209—215 see
Action on a projective module      16
Action on a space      13 see
Action on a tensor product      see "Tensor product"
Action on a vector bundle      13
Action, AF      287 see
Action, commuting      209—215 219 227—228
Action, exterior equivalent      44—40 53 55 134 135 139 141 198—199 206 212 219 227—228 296
Action, free      1—5 7—9 131—135 138—139 142—143 146 151 156—157 161—167 189 221—222 227 234 236 242—244 247—248 270 272 275 278—283 285 289—290 299 309
Action, hereditarily K-saturated      270—274 281 285 299
Action, hereditarily K-saturated up to 2-torsion      272
Action, hereditarily saturated      236—237 246—251 270—275 278 281—285 299—301
Action, inner      44
Action, K-free      136 see
Action, K-saturated      270—274 285
Action, KK-free      151 see
Action, locally representable      5 286 292—299 305 309 327—328
Action, outer      298 305
Action, product type      286 292—294 298—302 305 309
Action, restriction to subgroup of      3—5 137—138 143 162 177—182 272 288 300 302 305 307—309
Action, saturated      236—237 240—251 270 273—274 282
Action, totally K-free      138 see
Action, totally K-free up to torsion      178—179
Action, totally KK-free      152
Action, with discrete K-theory      132 153 157 163 262 270 290 293 306—309
Action, with discrete KK-theory      151—154 181 182 233 306—308 328
Action, with locally discrete K-theory      131—138 141 157 178 185 211 224 232 235 271 286—296 299 328
ad(u) (a $\longrightarrow$ u*au)      137
Additivity of KK-theory      325 326 see
AF action      267 286—320
AF action, discrete K-theory and      307 308 328
AF action, K-freeness of      5 206—294 298—305 309
AF action, KK-freeness of      5 286 307 308 328
AF action, locally discrete K-theory and      286—296 299 328
AF action, total K-freeness of      5 286 288—289 291 294—295 299 302 307 308—309 312
AF algebra      5 68 130 178 181 227—228 252 263 266 268—270 284 286—328 see
AF algebra, equivariant KK-theory of      68 308 328
AF algebra, K-visibility of      252
AF algebra, order on K-theory of      252 294 297 298 305
AF automorphism      290—291
AF G-algebra      287 286—328
Akemann, c.a.      120 122
Algebra, $(G,C_{0}(X))$ -      158—159 162—164 219 248 277 278
Algebra, $C_{0}(X)$ -      157—159 162—164 219 248 277 278
Algebra, (G,C(X))-      159—162 279
Algebra, AF G-      287 see
Algebra, C(X)-      76 159—162 278 279
Algebra, G-      15
Algebra, G-Banach      15—22 28—34 38 69
Amenable group      211 215
Approximate identity of projections, in crossed product      19
Approximate identity, quasicentral      81 84 87—89 93
Approximately inner automorphism      305
Artin's theorem      177 180
Arveson Spectrum      137—138 246 249 301
Atiyah, M.F.      1 6 7 8 9 10 24 26 56 58 68 108 109 110 111 112 113 114 115 141 152 156 179 196 216 296 326
Augmentation ideal      14
Aut(A) (automorphism group)      15
Automorphism, AF      290—291
Automorphism, approximately inner      305
Automorphism, inner      45
Automorphism, outer      236
Automorphism, universally weakly inner      283—284
Baire category theorem      8
Baire space      208 275—277
Banach *-algebraic bundle      240 244
Banach algebra      3 12 15—22 28—34 36—38 41 55 58 69
Baum, P.      2
Bimodule      236—241
Bimodule, Morita equivalence      236—240
Binomial coefficient      180 258 260
Blackadar, B.      33 34 305 306 313
Bott periodicity for K-theory      52 58
Bott periodicity for KK-theory      109—115
Bott periodicity, relation between maps for K- and KK-theory      129
Bratteli, O.      228 252 269 286 288 301 312
Brauer's theorem      180
Bredon, G.E.      7 10 147 151 163
Brown, L.G.      62 63 66 68 267
Bundle of C*-algebras      76 146 157
Bundle, Banach *-algebraic      240 244
Bundle, vector      2 6—8 12—15 23—27 110—115 129 156—157 189
Busby, R.C.      44
C(X) (continuous functions)      23
C(X)-algebra      76 159—162 278 279
C(X)-module      157 158
C(X)-module, locally convex      158
C(X,A) (continuous A-valued functions)      17
C*(G) (group C*-algebra)      49
C*(G,A) (crossed product)      see "C*(G src='/math_tex/c745b9b57c145ec5577b82542b2df54682.gif'
C*(G,A, $\alpha$ ) (crossed product)      18
C*-algebra valued inner product      42—43 117 238—241
C*-dynamical system      5
CA (cone)      54
Cauchy — Schwarz inequality      43
Change of group homomorphism      167 see "Restriction"
Choi, M.-D.      140
Circle group      19 30 133 156 165 190 212 216 228 263—265 274 275 280—283 285 289 301—303 309 312
Circle group, action of      133 156 165 190 228 263—265 274 275 280—283 285 301—302 309
Cocycle, one-      44 46 139 198 311
Cocycle, two-      155
Cohomology of sheaves      114
Cohomology theory, for C*-algebras      69 156 325
Cohomology theory, for spaces      1 55
Commuting actions      209—215 219 227—228
Compact operator on Hilbert module      117
Compactification, free      164—166
Compactification, one point      14
Complex conjugate representation      39 71 109 155 323—324
Complex projective space      110 156
Composition series      141—142 147 150 157 205 208 227 244 247 266 268 275 277—279
Conditional expectation      250
Conditional expectation, generalized      42
Cone over a C*-algebra      54 57 61 217—218
Cone, mapping      61 217—218
Conjugate representation      39 71 109 155 323—324
Connected group      2 59 71 113 189 262 284 309 314
Connecting homomorphism      48 53—55 57 60—61 191 196 204
Connes Isomorphism Theorem (Connes' Thom Isomorphism Theorem), in equivariant K-theory      190 209 210 214
Connes spectrum      4 131 137—138 236 249 250 263—264 282 301 305
Connes spectrum, strong      4—5 212 227 236—237 249—250 257—263 283 286 305
Connes, A.      2 190 209 210
Continuity of K-theory      34—36 53
Continuity of KK-theory      158 325
Continuous field of C*-algebras      164 208 281
Continuous field of C*-algebras, locally trivial      208
Continuous trace algebra      208 285

1 2 3 4

О проекте