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Book Review

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Book Information:

Author: Alain Connes
Title: Noncommutative geometry
Additional book information: Academic Press, Paris, 1994, xiii+661 pp., ISBN 0-12-185860-X
Originally published in French by InterEditions, Paris (Geometrie Non Commutative, 1990)

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

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  • 2. E. Wigner, On unitary representations of the inhomogeneous Lorentz group, Ann. Math. 40 (1939), 149--204.
  • 3. J. von Neumann, Zur Algebra der Funktionoperatoren, Math. Ann. 102 (1929), 370--427.
  • 4. I. E. Segal and Z. Zhou, Convergence of quantum electrodynamics in a curved deformation of Minkowski space, Ann. Physics 232 (1994), no. 1, 61–87. MR 1276089, https://doi.org/10.1006/aphy.1994.1050
  • 5. J. Pedersen, I. E. Segal, and Z. Zhou, Nonlinear quantum fields in ≥4 dimensions and cohomology of the infinite Heisenberg group, Trans. Amer. Math. Soc. 345 (1994), no. 1, 73–95. MR 1204416, https://doi.org/10.1090/S0002-9947-1994-1204416-7
  • 6. I. Segal, Rigorous covariant form of the correspondence principle, Proceedings, 1994 J. von Neumann Symposium (W. Arveson, T. Branson, I. Segal, eds.), Amer. Math. Soc., Providence, RI, 1996, 175--202.
  • 7. ------, Complex noncommutative infinite-dimensional analysis, Proceedings, 1994 Norbert Wiener Symposium (D. Jerison, I. Singer, and D. Stroock, eds.) (in preparation).
  • 8. ------, A non-commutative extension of abstract integration, Ann. Math. (2) 57 (1953), 401--457. MR 14:991f
  • 9. ------, An extension of Plancherel's theorem to separable unimodular groups, Ann. Math. (2) 52 (1950), 272--292. MR 12:157f
  • 10. ------, Decompositions of operator algebras, Mem. Amer. Math. Soc. No. 9 (1951). MR 13:472b
  • 11. ------, A class of operator algebras which are determined by groups, Duke Math. J. 18 (1951), 221--265. MR 13:534b
  • 12. ------, Irreducible representations of operator algebras, Bull. Amer. Math. Soc. 53 (1947), 73--88. MR 8:520b
  • 13. J. von Neumann, Continuous geometry, Proc. Nat. Acad. Sci. U.S.A. 22 (1936), 92--100.
  • 14. H. A. Dye, The Radon-Nikodym theorem for finite rings of operators, Trans. Amer. Math. Soc. 72 (1952), 243--280. MR 13:662b

Review Information:

Reviewer: Irving Segal
Affiliation: Massachusetts Institute of Technology
Journal: Bull. Amer. Math. Soc. 33 (1996), 459-465
DOI: https://doi.org/10.1090/S0273-0979-96-00687-8
Review copyright: © Copyright 1996 American Mathematical Society