A Brief Introduction to Quantum GeometryTable of Contents
Introduction Literature | |
| [BR] | Brateli O, Robinson D: Operator Algebras and Quantum Statistical Mechanics, Volumes 1/2, Springer-Verlag (1979) |
| [BDF] | Brown L G, Douglas R G, Filmore P G: Extensions of C*-algebras and K-Homology, Ann Math, 105 265-324 (1977) |
| [C1] | Connes A: Non-commutative differential geometry, Extrait des Publications Mathematiques--IHES 62 (1986) |
| [C2] | Connes A: Noncommutative Geometry, Academic Press (1994) |
| [Dx] | Dixmier J: Les algebres d'operateurs dans l'espace Hilbertien, Gauthier-Villars (1957) |
| [DubV] | Dubois-Violette: Derivations et calcul differentiel non-commutatif, CR Acad Sci Paris 307 (1988) |
| [DKM1] | Dubois-Violette, R Kerner, J Madore: Noncommutative Differential Geometry of Matrix Algebras, J Math Phys 31 316-322 (1990) |
| [DKM2] | Dubois-Violette, R Kerner, J Madore: Noncommutative Differential Geometry and New Models of Gauge Theory, J Math Phys 31 323-335 (1990) |
| [D1] | Durdevich M: Geometry of Quantum Principal Bundles I, Commun Math Phys 175 (3) 457-521 (1996) |
| [D2] | Durdevich M: Geometry of Quantum Principal Bundles II, Rev Math Phys 9 (5) 531-607 (1997) |
| [D3] | Durdevich M: Algebro-Geometric Constructions of Subquantum Theories, Doctoral Thesis, Faculty of Physics, University of Belgrade, Serbia [in Serbian :)] (1993) |
| [F] | Fedosov B: Deformation Quantization and Index Theory, Akademie Verlag GmbH, Berlin (1996) |
| [K1] | Kastler D: Cyclic Cohomology Within Differential Envelope, Hermann, Paris (1988) |
| [K2] | Kastler D: Introduction to Alain Connes' Non-Commutative Differential Geometry, Karpacz Lectures (1986) |
| [Mad] | Madore J: An Introduction to Noncommutative Differential Geometry and Its Physical Applications, Book--Second Edition (1998) |
| [MvN1] | Murray F J, von Neumann J: On Rings of Operators, Ann Math 37 116-229 (1936) |
| [MvN2] | Murray F J, von Neumann J: On Rings of Operators 2, Trans Amer Math Soc 41 208-248 (1937) |
| [MvN4] | Murray F J, von Neumann J: On Rings of Operators 4, Ann Math {\bf 44} 716-808 (1943) |
| [P] | Podles P: Quantum Spheres, Lett Math Phys 14 193-202 (1987) |
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| [SV1] | Sanchez-Valenzuela O A: On Supergeometric Structures, Ph.D.Thesis, Harvard University, Cambridge (1986) |
| [SV2] | Sanchez-Valenzuela O A: Differential-Geometric Approach to Supervector Bundles, Preprint, CIMAT, Guanajuato, Mexico (1996) |
| [R] | Rothstein M: The Axioms of Supermanifolds and a New Structure Arising From Them, Trans Amer Math Soc 297 159-180 (1986) |
| [We] | Wegge-Olsen N E: K-Theory and C*-Algebras, Oxford Science Publications (1993) |
| [W1] | Woronowicz S L: Pseudospaces, Pseudogroups and Pontryagin duality, Lecture Notes in Physics 116, Proceedings of the International Conference on Mathematical Physics, Lausanne (1979) |
| [W2] | Woronowicz S L: C*-algebras Generated by Unbounded Elements, Rev Math Phys, 7 (3) 481-521 (1995) |
| [W3] | Woronowicz S L: Twisted SU(2) group; An example of a noncommutative differential calculus, RIMS, Kyoto University 23, 117-181 (1987) |
| [W4] | Woronowicz S L: Compact Matrix Pseudogroups, Commun Math Phys 111, 613-665 (1987) |
| [W5] | Woronowicz S L: Differential Calculus on Compact Matrix Pseudogroups (Quantum Groups), Commun Math Phys 122, 125-170 (1989) |
| [W6] | Woronowicz S L: Tannaka-Krein Duality for Compact Matrix Pseudogroups; Twisted SU(n) groups, Invent Math 93, 35-76 (1988) |
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