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Book Review

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Book Information:

Author: N. Christopher Phillips
Title: Equivariant $K$-theory and freeness of group actions on $C^*$-algebras
Additional book information: Lecture Notes in Math., vol. 1274, Springer-Verlag, Berlin and New York, viii + 371 pp., $32.90. ISBN 3-540-18277-2.

References [Enhancements On Off] (What's this?)

  • 1. B. Blackadar, Operator algebras, Encyclopaedia of Mathematical Sciences, vol. 122, Springer-Verlag, Berlin, 2006. Theory of 𝐶*-algebras and von Neumann algebras; Operator Algebras and Non-commutative Geometry, III. MR 2188261
  • 2. L. Brown, R. Douglas and P. Fillmore, Extensions of C*-algebras and K-homology, Ann. of Math. (2) 105 (1977), 265-324. MR 458196
  • 3. A. Connes, A survey of foliations and operator algebras, Operator algebras and applications, Part I (Kingston, Ont., 1980) Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, R.I., 1982, pp. 521–628. MR 679730
  • 4. Alain Connes, Noncommutative differential geometry, Inst. Hautes Études Sci. Publ. Math. 62 (1985), 257–360. MR 823176
  • 5. Joachim Cuntz, 𝐾-theory for certain 𝐶*-algebras, Ann. of Math. (2) 113 (1981), no. 1, 181–197. MR 604046, https://doi.org/10.2307/1971137
  • 6. G. Elliott, On the classification of inductive limits of sequences of semi-simple finite dimensional algebras, J. Algebra 38 (1976), 29-44. MR 397420
  • 7. M. Karoubi, K-theory: An introduction, Springer-Verlag, Berlin and New York, 1978. MR 488029
  • 8. G. G. Kasparov, The operator 𝐾-functor and extensions of 𝐶*-algebras, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), no. 3, 571–636, 719 (Russian). MR 582160
  • 9. G. G. Kasparov, Equivariant 𝐾𝐾-theory and the Novikov conjecture, Invent. Math. 91 (1988), no. 1, 147–201. MR 918241, https://doi.org/10.1007/BF01404917
  • 10. M. Pimsner and D. Voiculescu, Exact sequences for 𝐾-groups and Ext-groups of certain cross-product 𝐶*-algebras, J. Operator Theory 4 (1980), no. 1, 93–118. MR 587369

Review Information:

Reviewer: Joachim Cuntz
Journal: Bull. Amer. Math. Soc. 20 (1989), 101-103
DOI: https://doi.org/10.1090/S0273-0979-1989-15715-7
American Mathematical Society