1 Compact Quantum Groups, (CQG) s

A compact quantum group, Q_CG is defined as a particular case of a locally compact quantum group Q_Glc when the object space of the latter Q_Glc is a compact topological space (instead of being a locally compact one).

Bibliography

[1] ABE, E., Hopf Algebras, Cambridge University Press, 1977.

[2] BAAJ, S., SKANDALIS, G., Unitaires multiplicatifs et dualité pour les produits croisés de C*-algébres, Ann. scient. Ec. Norm. Sup., 4e série, t. 26 (1993), 425-488.

[3] CONWAY, J. B., A Course in Functional Analysis, Springer-Verlag, New York, 1985.

[4] DIJKHUIZEN, M.S., KOORNWINDER, T.H., CQG algebras : a direct algebraic approach to quantum groups, Lett. Math. Phys. 32 (1994), 315-330.
[5] DIXMIER, J., C*-algebras, North-Holland Publishing Company, Amsterdam, 1982.
[6] ENOCK, M., SCHWARTZ, J.-M., Kac Algebras and duality of Locally Compact Groups, Springer-Verlag, Berlin (1992).
[7] EFFROS, E.G., RUAN, Z.-J., Discrete Quantum Groups I. The Haar measure, Int. J. of Math. (1994), 681-723.
[8] HOFMANN, K.H., Elements of compact semi-groups, Charles E. Merill Books Inc. Columbus, Ohio (1996).
[9] HOLLEVOET, J., Lokaal compacte quantum-semigroepen : Representaties en Pontryagin-dualiteit, Ph.D. Thesis, K.U.Leuven, 1994.
[10] HOLLEVOET, J., Pontryagin Duality for a Class of Locally Compact Quantum Groups, Math. Nachrichten 176 (1995), 93-110.
[11] KIRCHBERG, E., Discrete Quantum Groups, talk at Oberwolfach, 1994.
[12] KUSTERMANS, J., C*-algebraic Quantum Groups arising from Algebraic Quantum Groups, Ph.D. Thesis, K.U.Leuven, 1997.
[13] KUSTERMANS, J., VAN DAELE, A., C*-algebraic Quantum Groups arising from Algebraic Quantum Groups, Int. J. of Math. 8 (1997), 1067-1139.
[14] LANCE, E.C., An explicit description of the fundamental unitary for SU(2)q, Commun. Math. Phys. 164 (1994), 1-15.
[15] DE MAGELHAES, I.V., Hopf-C*-algebras and locally compact groups, Pacific J. Math (2) 36 (1935), 448-463.
[16] 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.
[17] MASUDA, M., A C*-algebraic framework for the quantum groups, talk at Warsaw workshop on Quantum Groups and Quantum Spaces, 1995.
[18] MASUDA, M., NAKAGAMI, Y., WORONOWICZ, , S.L. (in preparation).
[19] SHEU, A.J.L., Compact Quantum Groups and groupoid C*-Algebras, J. Funct. Analysis 144 (1997), 371-393.
[20] SWEEDLER, M.E., Hopf Algebras, W.A. Benjamin, inc., New York, 1969.
[21] TOMIYAMA, J., Applications of Fubini type theorems to the tensor product of C*-algebras, Tokohu Math. J. 19 (1967), 213-226.
[22] VAN DAELE, A., Dual Pairs of Hopf *-algebras, Bull. London Math. Soc. 25 (1993), 209-230.
[23] VAN DAELE, A., Multiplier Hopf Algebras, Trans. Am. Math. Soc. 342 (1994), 917-932. [24] VAN DAELE, A., The Haar Measure on a Compact Quantum Group, Proc. Amer. Math. Soc. 123 (1995), 3125-3128. [25] VAN DAELE, A., Discrete Quantum Groups, Journal of Algebra 180 (1996), 431-444. [26] VAN DAELE, A., An Algebraic Framework for Group Duality, preprint K.U.Leuven (1996), to appear in Advances of Mathematics.
[27] 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.
[28] VAN DAELE, A., The Haar measure on finite quantum groups, Proc. A.M.S. 125 (1997), 3489-3500.
[29] VAN DAELE, A., WANG, S., Universal Quantum Groups, Int. J. of Math. (1996), 255-263. [30] WANG, S., Krein Duality for Compact Quantum Groups, J. Math. Phys. 38 (1997), 524-534.
31. WORONOWICZ, S.L., Twisted SU(2) group. An example of non-commutative differential calculus. Publ. RIMS Kyoto Univ. 23 No. 1 (1987), 117-181.
[32] 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 SU(n) groups, Invent. Math. 93 (1988) 35-76. [34] WORONOWICZ, S.L., A remark on Compact Matrix Quantum Groups, Lett. Math. Phys. 21 (1991), 35-39. [35] WORONOWICZ, S.L., Compact Quantum Groups, Preprint University ofWarszawa (1992). To appear.
36. MAES, A. and VanDAELE, A. 1998. Notes on Compact Quantum Groups., arxiv.org.math − FA − 9803122v1, 43 pp.