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Book Review
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Book Information
Author(s):
Alain Connes
Title:
Noncommutative geometry
Additional book information:
Academic Press,
Paris,
1994,
xiii+661,
0-12-185860-X; originally published in French by InterEditions, Paris (Geometrie Non Commutative, 1990)
References:
- 1.
- J. von Neumann, Die Eindeutigket der Schrodingerschen Operatoren, Math. Ann. 104 (1931), 570--578.
- 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. Segal and Z. Zhou, Convergence of quantum electrodynamics in a curved deformation of Minkowski space, Ann. Phys. 232 (1994), 61--87. MR 95c:81174
- 5.
- J. Pedersen, I. Segal, and Z. Zhou, Nonlinear quantum fields in
4 dimensions and cohomology of the infinite Heisenberg group, Trans. Amer. Math. Soc. 345 (1994), 73--95. MR 95a:81158 - 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
Additional Information:
Reviewer(s):
Irving
Segal
Affiliation:
Massachusetts Institute of Technology
Review Information:
Journal:
Bull. Amer. Math. Soc.
33
(1996),
459-465.
MSC
(1991):
Primary 82Exx
DOI:
10.1090/S0273-0979-96-00687-8
PII:
S 0273-0979(96)00687-8
Copyright of article:
Copyright
1996,
American Mathematical Society
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