PlanetPhysics/Compact Quantum Groups
Compact Quantum Groups, (CQG) s
editA compact quantum group, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle Q_{CG'' } } is defined as a particular case of a locally compact quantum group when the object space of the latter is a compact topological space (instead of being a locally compact one).
Bibliography
ABE, E., Hopf Algebras, Cambridge University Press, 1977.
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BAAJ, S., SKANDALIS, G., Unitaires multiplicatifs et dualit\'e pour les produits crois\'es de C*-alg\'ebres, Ann. scient. Ec. Norm. Sup., 4e s\'erie, t. 26 (1993), 425-488.
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CONWAY, J. B., A Course in Functional Analysis, Springer-Verlag, New York, 1985.
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DIJKHUIZEN, M.S., KOORNWINDER, T.H., CQG algebras : a direct algebraic approach to quantum groups, Lett. Math. Phys. 32 (1994), 315-330.\\ DIXMIER, J., C*-algebras, North-Holland Publishing Company, Amsterdam, 1982.\\ ENOCK, M., SCHWARTZ, J.-M., Kac Algebras and duality of Locally Compact groups, Springer-Verlag, Berlin (1992).\\ EFFROS, E.G., RUAN, Z.-J., Discrete Quantum Groups I. The Haar measure, Int. J. of Math. (1994), 681-723.\\ HOFMANN, K.H., Elements of compact semi-groups, Charles E. Merill Books Inc. Columbus, Ohio (1996).\\ HOLLEVOET, J., Lokaal compacte quantum-semigroepen : Representaties en Pontryagin-dualiteit, Ph.D. Thesis, K.U.Leuven, 1994.\\ HOLLEVOET, J., Pontryagin Duality for a Class of Locally Compact Quantum Groups, Math. Nachrichten 176 (1995), 93-110.\\ KIRCHBERG, E., Discrete Quantum Groups, talk at Oberwolfach, 1994.\\ KUSTERMANS, J., C*-algebraic Quantum Groups arising from Algebraic Quantum Groups, Ph.D. Thesis, K.U.Leuven, 1997.\\ KUSTERMANS, J., VAN DAELE, A., C*-algebraic Quantum Groups arising from Algebraic Quantum Groups, Int. J. of Math. 8 (1997), 1067-1139.\\ LANCE, E.C., An explicit description of the fundamental unitary for SU(2)q, Commun. Math. Phys. 164 (1994), 1-15.\\ DE MAGELHAES, I.V., Hopf-C*-algebras and locally compact groups, Pacific J. Math (2) 36 (1935), 448-463.\\ MASUDA, M., NAKAGAMI, Y., A von Neumann algebra Framework for the Duality of Quantum Groups. Publications of the RIMS Kyoto University 30 (1994), 799-850.\\ MASUDA, M., A C*-algebraic framework for the quantum groups, talk at Warsaw workshop on Quantum Groups and Quantum Spaces, 1995.\\ MASUDA, M., NAKAGAMI, Y., WORONOWICZ, , S.L. (in preparation).\\ SHEU, A.J.L., Compact Quantum Groups and groupoid C*-Algebras, J. Funct. Analysis 144 (1997), 371-393.\\ SWEEDLER, M.E., Hopf Algebras, W.A. Benjamin, inc., New York, 1969.\\ TOMIYAMA, J., Applications of Fubini type theorems to the tensor product of C*-algebras, Tokohu Math. J. 19 (1967), 213-226.\\ VAN DAELE, A., Dual Pairs of Hopf *-algebras, Bull. London Math. Soc. 25 (1993), 209-230.\\ VAN DAELE, A., Multiplier Hopf Algebras, Trans. Am. Math. Soc. 342 (1994), 917-932. VAN DAELE, A., The Haar Measure on a Compact Quantum Group, Proc. Amer. Math. Soc. 123 (1995), 3125-3128. VAN DAELE, A., Discrete Quantum Groups, Journal of Algebra 180 (1996), 431-444. VAN DAELE, A., An Algebraic Framework for Group Duality, preprint K.U.Leuven (1996), to appear in Advances of Mathematics. \\ VAN DAELE, A., Multiplier Hopf Algebras and Duality, Proceedings of the workshop on Quantum Groups and Quantum Spaces in Warsaw (1995), Polish Academy of sciences Warszawa 40 (1997), 51-58.\\ VAN DAELE, A., The Haar measure on finite quantum groups, Proc. A.M.S. 125 (1997), 3489-3500.\\ VAN DAELE, A., WANG, S., Universal Quantum Groups, Int. J. of Math. (1996), 255-263. WANG, S., Krein Duality for Compact Quantum Groups, J. Math. Phys. 38 (1997), 524-534.\\ 31. WORONOWICZ, S.L., Twisted group. An example of non-commutative differential calculus. Publ. RIMS Kyoto Univ. 23 No. 1 (1987), 117-181.\\ WORONOWICZ, S.L., Compact matrix Pseudogroups, Commun. Math. Phys. 111 (1987), 613-665.\\ 33. WORONOWICZ, S.L., Tannaka-Krein duality for compact matrix pseudogroups. Twisted groups, Invent. Math. 93 (1988) 35-76. WORONOWICZ, S.L., A remark on Compact Matrix Quantum Groups, Lett. Math. Phys. 21 (1991), 35-39. WORONOWICZ, S.L., Compact Quantum Groups, Preprint University ofWarszawa (1992). To appear.\\ 36. MAES, A. and VanDAELE, A. 1998. Notes on Compact Quantum Groups., , 43 pp.
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