Bulletin of the American Mathematical Society

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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)

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.

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J. von Neumann, Zur Algebra der Funktionoperatoren, Math. Ann. 102 (1929), 370--427.

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, DOI 10.1006/aphy.1994.1050

J. Pedersen, I. E. Segal, and Z. Zhou, Nonlinear quantum fields in $\geq 4$ dimensions and cohomology of the infinite Heisenberg group, Trans. Amer. Math. Soc. 345 (1994), no. 1, 73–95. MR 1204416, DOI 10.1090/S0002-9947-1994-1204416-7

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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).

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Charles Hopkins, Rings with minimal condition for left ideals, Ann. of Math. (2) 40 (1939), 712–730. MR 12, DOI 10.2307/1968951

C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13

C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13

A. R. Collar, On the reciprocation of certain matrices, Proc. Roy. Soc. Edinburgh 59 (1939), 195–206. MR 8

13.

J. von Neumann, Continuous geometry, Proc. Nat. Acad. Sci. U.S.A. 22 (1936), 92--100.

C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13

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

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12.

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J. von Neumann, Continuous geometry, Proc. Nat. Acad. Sci. U.S.A. 22 (1936), 92--100.

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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