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Volumn 122, Issue 2, 2004, Pages 233-280

Finite group actions on C*-algebras with the Rohlin property, I

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EID: 2442674101     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-04-12221-3     Document Type: Review
Times cited : (181)

References (61)
  • 1
    • 84966211102 scopus 로고
    • On the existence of central sequences in subfactors
    • MR 1005075
    • D. H. BISCH, On the existence of central sequences in subfactors, Trans. Amer. Math. Soc. 321 (1990), 117-128. MR 1005075
    • (1990) Trans. Amer. Math. Soc. , vol.321 , pp. 117-128
    • Bisch, D.H.1
  • 2
    • 0001502780 scopus 로고
    • Symmetries of the CAR algebra
    • MR 1053492
    • B. BLACKADAR, Symmetries of the CAR algebra, Ann. of Math. (2) 131 (1990), 589-623. MR 1053492
    • (1990) Ann. of Math. (2) , vol.131 , pp. 589-623
    • Blackadar, B.1
  • 3
    • 0003882539 scopus 로고    scopus 로고
    • K-theory for operator algebras, 2nd ed.
    • Cambridge Univ. Press, Cambridge. MR 1656031
    • _, K-Theoryfor Operator Algebras, 2nd ed., Math. Sci. Res. Inst. Publ. 5, Cambridge Univ. Press, Cambridge, 1998. MR 1656031
    • (1998) Math. Sci. Res. Inst. Publ. , vol.5
  • 4
    • 2442670045 scopus 로고    scopus 로고
    • talk at the Fields Institute, Waterloo, Canada, December 1994
    • _, talk at the Fields Institute, Waterloo, Canada, December 1994.
  • 5
    • 0000819152 scopus 로고
    • Approximately central matrix units and the structure of noncommutative tori
    • MR 1189278
    • B. BLACKADAR, A. KUMJIAN, and M. RØRDAM, Approximately central matrix units and the structure of noncommutative tori, K-Theory 6 (1992), 267-284. MR 1189278
    • (1992) K-Theory , vol.6 , pp. 267-284
    • Blackadar, B.1    Kumjian, A.2    Rørdam, M.3
  • 6
    • 0007299008 scopus 로고
    • On the classification of inductive limits of inner actions of a compact group
    • Current Topics in Operator Algebras (Nara, Japan, 1990), River Edge, N.J. MR 1193924
    • O. BRATTELI, G. A. ELLIOTT, D. E. EVANS, and A. KISHIMOTO, "On the classification of inductive limits of inner actions of a compact group" in Current Topics in Operator Algebras (Nara, Japan, 1990), World Sci., River Edge, N.J., 1991, 13-24. MR 1193924
    • (1991) World Sci. , pp. 13-24
    • Bratteli, O.1    Elliott, G.A.2    Evans, D.E.3    Kishimoto, A.4
  • 7
    • 0034385424 scopus 로고    scopus 로고
    • Trace scaling automorphisms of certain stable AF algebras, II
    • MR 1765786
    • O. BRATTELI and A. KISHIMOTO, Trace scaling automorphisms of certain stable AF algebras, II, Q. J. Math. 51 (2000), 131 -154. MR 1765786
    • (2000) Q. J. Math. , vol.51 , pp. 131-154
    • Bratteli, O.1    Kishimoto, A.2
  • 9
    • 0001188044 scopus 로고
    • Semicontinuity and multipliers of C*-algebras
    • MR 0969204
    • L. G. BROWN, Semicontinuity and multipliers of C*-algebras, Canad. J. Math. 40 (1988), 865-988. MR 0969204
    • (1988) Canad. J. Math. , vol.40 , pp. 865-988
    • Brown, L.G.1
  • 10
    • 0001523467 scopus 로고
    • Outer conjugacy classes of automorphisms of factors
    • MR 0394228
    • A. CONNES, Outer conjugacy classes of automorphisms of factors, Ann. Sci. École Norm. Sup. (4) 8 (1975), 383-419. MR 0394228
    • (1975) Ann. Sci. École Norm. Sup. (4) , vol.8 , pp. 383-419
    • Connes, A.1
  • 11
    • 0003372390 scopus 로고
    • 1
    • MR 0448101
    • 1, Acta Sci. Math. (Szeged) 39 (1977), 39-66. MR 0448101
    • (1977) Acta Sci. Math. (Szeged) , vol.39 , pp. 39-66
  • 12
    • 0002406227 scopus 로고
    • An analogue of the Thom isomorphism for crossed products of a C*-algebra by an action of ℝ
    • MR 0605351
    • _, An analogue of the Thom isomorphism for crossed products of a C*-algebra by an action of ℝ, Adv. in Math. 39 (1981), 31-55. MR 0605351
    • (1981) Adv. in Math. , vol.39 , pp. 31-55
  • 13
    • 3042722951 scopus 로고
    • Simple C*-algebras generated by isometries
    • MR 0467330
    • J. CUNTZ, Simple C*-algebras generated by isometries, Comm. Math. Phys. 57 (1977), 173-185. MR 0467330
    • (1977) Comm. Math. Phys. , vol.57 , pp. 173-185
    • Cuntz, J.1
  • 14
    • 0001106382 scopus 로고
    • K-theory for certain C*-algebras
    • MR 0604046
    • _, K-theory for certain C*-algebras, Ann. of Math. (2) 113 (1981), 181 -197. MR 0604046
    • (1981) Ann. of Math. (2) , vol.113 , pp. 181-197
  • 15
    • 2442691336 scopus 로고
    • Some remarks on the C*-algebras associated with certain topological Markov chains
    • MR 0631338
    • J. CUNTZ and D. E. EVANS, Some remarks on the C*-algebras associated with certain topological Markov chains, Math. Scand. 48 (1981), 235-240. MR 0631338
    • (1981) Math. Scand. , vol.48 , pp. 235-240
    • Cuntz, J.1    Evans, D.E.2
  • 16
    • 0001175308 scopus 로고
    • A class of C*-algebras and topological Markov chains
    • MR 0561974
    • J. CUNTZ and W. KRIEGER, A class of C*-algebras and topological Markov chains, Invent. Math. 56 (1980), 251-268. MR 0561974
    • (1980) Invent. Math. , vol.56 , pp. 251-268
    • Cuntz, J.1    Krieger, W.2
  • 17
    • 0003336982 scopus 로고
    • Dimensions and C*-algebras
    • Conf. Board Math. Sci., Washington, D.C. MR 0623762
    • E. G. EFFROS, Dimensions and C*-Algebras, CBMS Reg. Conf. Ser. Math. 46, Conf. Board Math. Sci., Washington, D.C., 1981. MR 0623762
    • (1981) CBMS Reg. Conf. Ser. Math. , vol.46
    • Effros, E.G.1
  • 18
    • 84941833127 scopus 로고
    • On the classification of C*-algebras of real rank zero
    • MR 1241132
    • G. A. ELLIOTT, On the classification of C*-algebras of real rank zero, J. Reine Angew. Math. 443 (1993), 179-219. MR 1241132
    • (1993) J. Reine Angew. Math. , vol.443 , pp. 179-219
    • Elliott, G.A.1
  • 19
    • 51249164213 scopus 로고
    • Classification of certain infinite simple C*-algebras, II
    • MR 1360606
    • G. A. ELLIOTT and M. RØRDAM, Classification of certain infinite simple C*-algebras, II, Comment. Math. Helv. 70 (1995), 615-638. MR 1360606
    • (1995) Comment. Math. Helv. , vol.70 , pp. 615-638
    • Elliott, G.A.1    Rørdam, M.2
  • 21
    • 0000785972 scopus 로고    scopus 로고
    • Trace scaling automorphisms of certain stable AF algebras
    • MR 1432548
    • D. E. EVANS and A. KISHIMOTO, Trace scaling automorphisms of certain stable AF algebras, Hokkaido Math. J. 26 (1997), 211-224. MR 1432548
    • (1997) Hokkaido Math. J. , vol.26 , pp. 211-224
    • Evans, D.E.1    Kishimoto, A.2
  • 23
    • 0001012859 scopus 로고
    • Sur la classification des symétries des C*-algèbres UHF
    • MR 0536360
    • TH. FACK AND O. MARÉCHAL, Sur la classification des symétries des C*-algèbres UHF, Canad. J. Math. 31 (1979), 496-523. MR 0536360
    • (1979) Canad. J. Math. , vol.31 , pp. 496-523
    • Fack, Th.1    Maréchal, O.2
  • 24
    • 0040991948 scopus 로고
    • Sur la classification des automorphismes périodiques des C*-algèbres UHF
    • MR 0611586
    • _, Sur la classification des automorphismes périodiques des C*-algèbres UHF, J. Funct. Anal. 40 (1981), 267-301. MR 0611586
    • (1981) J. Funct. Anal. , vol.40 , pp. 267-301
  • 27
    • 0038114866 scopus 로고
    • Product type actions of finite and compact groups
    • MR 0749311
    • D. HANDELMAN and W. ROSSMANN, Product type actions of finite and compact groups, Indiana Univ. Math. J. 33 (1984), 479-509. MR 0749311
    • (1984) Indiana Univ. Math. J. , vol.33 , pp. 479-509
    • Handelman, D.1    Rossmann, W.2
  • 28
    • 84972531306 scopus 로고
    • Actions of compact groups on AF C*-algebras
    • MR 0769758
    • _, Actions of compact groups on AF C*-algebras, Illinois J. Math. 29 (1985), 51-95. MR 0769758
    • (1985) Illinois J. Math. , vol.29 , pp. 51-95
  • 29
    • 0040972941 scopus 로고
    • Period two automorphisms of UHF C*-algebras
    • MR 0647069
    • R. H. HERMAN and V. F. R. JONES, Period two automorphisms of UHF C*-algebras, J. Funct. Anal. 45 (1982), 169-176. MR 0647069
    • (1982) J. Funct. Anal. , vol.45 , pp. 169-176
    • Herman, R.H.1    Jones, V.F.R.2
  • 30
    • 0039786317 scopus 로고
    • Models of finite group actions
    • MR 0702960
    • _, Models of finite group actions, Math. Scand. 52 (1983), 312 - 320. MR 0702960
    • (1983) Math. Scand. , vol.52 , pp. 312-320
  • 31
    • 0011677163 scopus 로고
    • Stability for integer actions on UHF C*-algebras
    • MR 0763780
    • R. H. HERMAN and A. OCNEANU, Stability for integer actions on UHF C*-algebras, J. Funct. Anal. 59 (1984), 132-144. MR 0763780
    • (1984) J. Funct. Anal. , vol.59 , pp. 132-144
    • Herman, R.H.1    Ocneanu, A.2
  • 32
    • 84972546610 scopus 로고
    • On a duality for C*-crossed products by a locally compact group
    • MR 0500719
    • S. IMAI and H. TAKAI, On a duality for C*-crossed products by a locally compact group, J. Math. Soc. Japan 30 (1978), 495-504. MR 0500719
    • (1978) J. Math. Soc. Japan , vol.30 , pp. 495-504
    • Imai, S.1    Takai, H.2
  • 33
    • 1942499699 scopus 로고    scopus 로고
    • The Rohlin property for automorphisms of C*-algebras
    • Mathematical Physics in Mathematics and Physics (Siena, Italy, 2000), Amer. Math. Soc., Providence. MR 1867556
    • M. IZUMI, "The Rohlin property for automorphisms of C*-algebras" in Mathematical Physics in Mathematics and Physics (Siena, Italy, 2000), Fields Inst. Commun. 30, Amer. Math. Soc., Providence, 2001, 191-206. MR 1867556
    • (2001) Fields Inst. Commun. , vol.30 , pp. 191-206
    • Izumi, M.1
  • 34
    • 0036258286 scopus 로고    scopus 로고
    • Inclusions of simple C*-algebras
    • MR 1900138
    • _, Inclusions of simple C*-algebras, J. Reine Angew. Math. 547 (2002), 97-138. MR 1900138
    • (2002) J. Reine Angew. Math. , vol.547 , pp. 97-138
  • 35
    • 0030163366 scopus 로고    scopus 로고
    • Purely infinite simple C*-crossed products, II
    • MR 1390356
    • J. A. JEONG, K. KODAKA, and H. OSAKA, Purely infinite simple C*-crossed products, II, Canad. Math. Bull. 39 (1996), 203-210. MR 1390356
    • (1996) Canad. Math. Bull. , vol.39 , pp. 203-210
    • Jeong, J.A.1    Kodaka, K.2    Osaka, H.3
  • 37
    • 0003512015 scopus 로고
    • The classification of purely infinite C*-algebras using Kasparov's theory
    • preprint, to appear
    • E. KIRCHBERG, The classification of purely infinite C*-algebras using Kasparov's theory, preprint, 1994, to appear in Fields Inst. Commun.
    • (1994) Fields Inst. Commun.
    • Kirchberg, E.1
  • 39
    • 85008107964 scopus 로고
    • On the fixed point algebra of a UHF algebra under a periodic automorphism of product type
    • MR 0500177
    • A. KISHIMOTO, On the fixed point algebra of a UHF algebra under a periodic automorphism of product type, Publ. Res. Inst. Math. Sci. 13 (1977/78), 777-791. MR 0500177
    • (1977) Publ. Res. Inst. Math. Sci. , vol.13 , pp. 777-791
    • Kishimoto, A.1
  • 40
    • 0001756927 scopus 로고
    • Actions of finite groups on certain inductive limit C*-algebras
    • MR 1078515
    • _, Actions of finite groups on certain inductive limit C*-algebras, Internat. J. Math. 1 (1990), 267-292. MR 1078515
    • (1990) Internat. J. Math. , vol.1 , pp. 267-292
  • 41
    • 0009360948 scopus 로고    scopus 로고
    • Automorphisms of AT algebras with the Rohlin property
    • MR 1660386
    • _, Automorphisms of AT algebras with the Rohlin property, J. Operator Theory 40 (1998), 277-294. MR 1660386
    • (1998) J. Operator Theory , vol.40 , pp. 277-294
  • 42
    • 0000569252 scopus 로고    scopus 로고
    • Unbounded derivations in AT algebras
    • MR 1658684
    • _, Unbounded derivations in AT algebras, J. Funct. Anal. 160 (1998), 270-311. MR 1658684
    • (1998) J. Funct. Anal. , vol.160 , pp. 270-311
  • 43
    • 0000707245 scopus 로고    scopus 로고
    • Crossed products of Cuntz algebras by quasi-free automorphisms
    • Operator Algebras and Their Applications (Waterloo, Ontario, Canada, 1994/1995), Amer. Math. Soc., Providence. MR 1424962
    • A. KISHIMOTO and A. KUMJIAN, "Crossed products of Cuntz algebras by quasi-free automorphisms" in Operator Algebras and Their Applications (Waterloo, Ontario, Canada, 1994/1995), Fields Inst. Commun. 13, Amer. Math. Soc., Providence, 1997, 173-192. MR 1424962
    • (1997) Fields Inst. Commun. , vol.13 , pp. 173-192
    • Kishimoto, A.1    Kumjian, A.2
  • 44
    • 0012810913 scopus 로고    scopus 로고
    • An introduction to the classification of amenable C*-algebras
    • River Edge, N.J., MR 1884366
    • H. LIN, An Introduction to the Classification of Amenable C*-Algebras, World Sci., River Edge, N.J., 2001. MR 1884366
    • (2001) World Sci.
    • Lin, H.1
  • 46
    • 84971678137 scopus 로고
    • Representations of finite groups and Cuntz-Krieger algebras
    • MR 1183780
    • M. H. MANN, I. RAEBURN, and C. E. SUTHERLAND, Representations of finite groups and Cuntz-Krieger algebras, Bull. Austral. Math. Soc. 46 (1992), 225-243. MR 1183780
    • (1992) Bull. Austral. Math. Soc. , vol.46 , pp. 225-243
    • Mann, M.H.1    Raeburn, I.2    Sutherland, C.E.3
  • 47
    • 84963043585 scopus 로고
    • Central sequences and the hyperfinite factor
    • MR 0281018
    • D. MCDUFF, Central sequences and the hyperfinite factor, Proc. London Math. Soc. (3) 21 (1970), 443-461. MR 0281018
    • (1970) Proc. London Math. Soc. (3) , vol.21 , pp. 443-461
    • McDuff, D.1
  • 48
    • 0003254555 scopus 로고
    • Duality for crossed products of von Neumann algebras
    • Springer, Berlin. MR 0546058
    • Y. NAKAGAMI and M. TAKESAKI, Duality for Crossed Products of von Neumann Algebras, Lecture Notes in Math. 731, Springer, Berlin, 1979. MR 0546058
    • (1979) Lecture Notes in Math. , vol.731
    • Nakagami, Y.1    Takesaki, M.2
  • 49
    • 0034366172 scopus 로고    scopus 로고
    • Aperiodic automorphisms of nuclear purely infinite simple C*-algebras
    • MR 1804956
    • H. NAKAMURA, Aperiodic automorphisms of nuclear purely infinite simple C*-algebras, Ergodic Theory Dynam. Systems 20 (2000), 1749 -1765. MR 1804956
    • (2000) Ergodic Theory Dynam. Systems , vol.20 , pp. 1749-1765
    • Nakamura, H.1
  • 50
    • 0003229160 scopus 로고
    • Actions of discrete amenable groups on von Neumann algebras
    • Springer, Berlin. MR 0807949
    • A. OCNEANU, Actions of Discrete Amenable Groups on von Neumann Algebras, Lecture Notes in Math. 1138, Springer, Berlin, 1985. MR 0807949
    • (1985) Lecture Notes in Math. , vol.1138
    • Ocneanu, A.1
  • 51
    • 0003216501 scopus 로고
    • C*-algebras and their automorphism groups
    • Academic Press, London. MR 0548006
    • G. K. PEDERSEN, C*-Algebras and Their Automorphism Groups, London Math. Soc. Monogr. 14, Academic Press, London, 1979. MR 0548006
    • (1979) London Math. Soc. Monogr. , vol.14
    • Pedersen, G.K.1
  • 52
    • 0002924111 scopus 로고    scopus 로고
    • A classification theorem for nuclear purely infinite simple C*-algebras
    • MR 1745197
    • N. C. PHILLIPS, A classification theorem for nuclear purely infinite simple C*-algebras, Doc. Math. 5 (2000), 49-114. MR 1745197
    • (2000) Doc. Math. , vol.5 , pp. 49-114
    • Phillips, N.C.1
  • 53
    • 0002819043 scopus 로고
    • Exact sequences for K-groups and Ext-groups of certain cross-product C*-algebras
    • MR 0587369
    • M. PIMSNER and D. VOICULESCU, Exact sequences for K-groups and Ext-groups of certain cross-product C*-algebras, J. Operator Theory 4 (1980), 93 -118. MR 0587369
    • (1980) J. Operator Theory , vol.4 , pp. 93-118
    • Pimsner, M.1    Voiculescu, D.2
  • 54
    • 84961488589 scopus 로고
    • Classification of inductive limits of Cuntz algebras
    • MR 1225963
    • M. RØRDAM, Classification of inductive limits of Cuntz algebras, J. Reine Angew. Math. 440 (1993), 175-200. MR 1225963
    • (1993) J. Reine Angew. Math. , vol.440 , pp. 175-200
    • Rørdam, M.1
  • 55
    • 11244255090 scopus 로고    scopus 로고
    • Classification of nuclear C*-algebras: Entropy in operator algebras
    • Operator Algebras and Non-commutative Geometry 7, Springer, Berlin. MR 1878881
    • M. RØRDAM and E. STØRMER, Classification of Nuclear C*-algebras: Entropy in Operator Algebras, Encyclopaedia Math. Sci. 126, Operator Algebras and Non-commutative Geometry 7, Springer, Berlin, 2001. MR 1878881
    • (2001) Encyclopaedia Math. Sci. , vol.126
    • Rørdam, M.1    Størmer, E.2
  • 56
    • 84972574152 scopus 로고
    • The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor
    • MR 0894590
    • J. ROSENBERG and C. SCHOCHET, The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor, Duke Math. J. 55 (1987), 431-474. MR 0894590
    • (1987) Duke Math. J. , vol.55 , pp. 431-474
    • Rosenberg, J.1    Schochet, C.2
  • 57
    • 84972496661 scopus 로고
    • Topological methods for C*-algebras, II: Geometry resolutions and the Künneth formula
    • MR 0650021
    • C. SCHOCHET, Topological methods for C*-algebras, II: Geometry resolutions and the Künneth formula, Pacific J. Math. 98 (1982), 443-458. MR 0650021
    • (1982) Pacific J. Math. , vol.98 , pp. 443-458
    • Schochet, C.1
  • 58
    • 84972569226 scopus 로고
    • Topological methods for C*-algebras IV: Mod p homology
    • MR 0757511
    • _, Topological methods for C*-algebras, IV: Mod p homology, Pacific J. Math. 114 (1984), 447-468. MR 0757511
    • (1984) Pacific J. Math. , vol.114 , pp. 447-468
  • 59
    • 21444449120 scopus 로고    scopus 로고
    • 2 actions on real rank zero C*-algebras
    • MR 1376557
    • 2 actions on real rank zero C*-algebras, Trans. Amer. Math. Soc. 348 (1996), 4199-4230. MR 1376557
    • (1996) Trans. Amer. Math. Soc. , vol.348 , pp. 4199-4230
    • Su, H.1
  • 60
    • 84996015847 scopus 로고
    • Cohomology and extensions of von Neumann algebras, II
    • MR 0574031
    • C. E. SUTHERLAND, Cohomology and extensions of von Neumann algebras, II, Publ. Res. Inst. Math. Sci. 16 (1980), 135 -174. MR 0574031
    • (1980) Publ. Res. Inst. Math. Sci. , vol.16 , pp. 135-174
    • Sutherland, C.E.1
  • 61
    • 0002171441 scopus 로고
    • On a duality for crossed products of C*-algebras
    • MR 0365160
    • H. TAKAI, On a duality for crossed products of C*-algebras, J. Funct. Anal. 19 (1975), 25-39. MR 0365160
    • (1975) J. Funct. Anal. , vol.19 , pp. 25-39
    • Takai, H.1


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