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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

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:

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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 $\ge $ 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.

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------, Complex noncommutative infinite-dimensional analysis, Proceedings, 1994 Norbert Wiener Symposium (D. Jerison, I. Singer, and D. Stroock, eds.) (in preparation).

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------, A non-commutative extension of abstract integration, Ann. Math. (2) 57 (1953), 401--457. MR 14:991f

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------, An extension of Plancherel's theorem to separable unimodular groups, Ann. Math. (2) 52 (1950), 272--292. MR 12:157f

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------, Decompositions of operator algebras, Mem. Amer. Math. Soc. No. 9 (1951). MR 13:472b

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------, A class of operator algebras which are determined by groups, Duke Math. J. 18 (1951), 221--265. MR 13:534b

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------, Irreducible representations of operator algebras, Bull. Amer. Math. Soc. 53 (1947), 73--88. MR 8:520b

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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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