A remark on Gel'fand duality for spectral triples

키워드

참고문헌 (38)

1. "Categories, quantization and much more"[URL]
2. M. Barr, "Category Theory for Computing Science, third edition" (1999), Centre de Recherches Mathematiques
3. N. Berline, "Heat Kernels and Dirac Operators" (1992), Springer-Verlag
4. P. Bertozzini, "Categories Logic and Physics", Categories of spectral geometries, Seminar Slides and Video of the Talk at the (2008)
5. P. Bertozzini, "A category of spectral triples and discrete groups with length function", Osaka J. Math, 43(2), pp.327~350 (2006)
6. P. Bertozzini, "Non-commutative geometry, categories and quantum physics", East-West J. Math, pp.213~259 (2007)
7. A. Connes, "Noncommutative Geometry" (1994), Academic Press
8. A. Connes, "Noncommutative geometry and reality", J. Math. Phys, 36(11), pp.6194~6231 (1995)
9. A. Connes, "Gravity coupled with matter and the foundation of non-commutative geometry", Comm. Math. Phys, 182(1), pp.155~176 (1996)
10. A. Connes, "Brisure de symetrie spontanee et geometrie du pont de vue spectral", J. Geom. Phys, 23(3), pp.206~234 (1997)
11. A. Connes, "On the spectral characterization of manifolds, arXiv:0810.2088", ~
12. A. Connes, "A unitary invariant in Riemannian geometry", Int. J. Geom. Methods Mod. Phys, 5(8), pp.1215~1242 (2008)
13. I. Dolgachev, "Book Review: The Geometry of Schemes", Bull. Amer. Math. Soc. (N.S.), 38(4), pp.467~473 (2001), Springer
14. S. Doplicher, "A new duality theory for compact groups", Invent. Math, 98(1), pp.157~218 (1989)
15. I. Gel'fand, "Normierte ringe", Mat. Sbornik, 51(9), pp.3~24 (1941)
16. I. Gel'fand, "On the imbedding of normed rings into the ring of operators in Hilbert space", Math. Sbornik, 12(54), pp.197~213 (1943)
17. J.-M. Gracia-Bondia, "Elements of Noncommutative Geometry" (2001), Birkhauser
18. P. Halmos, "Operator Methods in Classical Mechanics II", Ann. Math, 43, pp.332~350 (1942)
19. D. Hilbert, "Uber die vollen Invariantesysteme", Math. Ann, 42(3), pp.313~373 (1893)
20. M. Krein, "A principle of duality for bicompact groups and quadratic block algebras", Doklady Acad. Nauk SSSR (N. S.), 69, pp.725~728 (1949)
21. H.-B. Lawson, "Spin Geometry" (1989), Princeton University Press
22. S. MacLane, "Categories for the Working Mathematician" (1998), Springer
23. B. Mesland, "Unbounded biviariant K-theory and correspondences in noncommutative geometry", ~
24. P.Petersen, "Riemannian Geometry" (1998), Springer-Verlag
25. L. Pontryagin, "The theory of topological commutative groups", Ann. Math, 35(2), pp.361~388 (1934)
26. A. Rennie, "Commutative geometries are spin manifolds", Rev. Math. Phys, 13(4), pp.409~464 (2001)
27. A. Rennie, "Reconstruction of manifolds in noncommutative geometry", ~
28. A. Rennie, "Orbifolds are not commutative geometries", J. Aust. Math. Soc, 84(1), pp.109~116 (2008)
29. M.-A. Rieffel, "Compact quantum metric spaces, Operator algebras, quantization, and noncommutative geometry", Contemp. Math, 365, pp.315~330 (2004), Amer. Math. Soc
30. On the definition of geometric Dirac operators, "H. Schroder", ~
31. J.-P. Serre, "Modules projectifs et espaces fibr a fibre vectorielle, expose 23" (1958), Seminaire Dubreil-Pisot
32. M. Stone, "The theory of representations for Boolean algebras", Trans. Amer. Math. Soc, 40(1), pp.37~111 (1936)
33. M. Stone, "Applications of the theory of Boolean rings to general topology", Trans. Amer. Math. Soc, 41(3), pp.375~481 (1937)
34. R. Swan, "Vector bundles and projective modules", Trans. Amer. Math. Soc, 105, pp.264~277 (1962)
35. A. Takahashi, "Hilbert modules and their representation", Rev. Colombiana Mat, 13(1), pp.1~38 (1979)
36. A. Takahashi, "A duality between Hilbert modules and fields of Hilbert spaces", Rev. Colombiana Mat, 13(2), pp.93~120 (1979)
37. T. Tannaka, "Uber den dualitatssatz der nichtkommutativen topologischen gruppen", Tohoku Math. J, 45, pp.1~12 (1939)
38. E. van Kampen, "Locally bicompact abelian groups and their character groups", Ann. Math, 36(2), pp.448~463 (1935)

관련 논문AI추천