Center of the algebra of functions on the quantum group SU_q(2) and related topics

• Autorzy: Krajczok J. , Sołtan P.

Identyfikatory

DOI

10.14708/cm.v56i2.1557

• Języki publikacji: EN

Abstrakty

EN

The center of the algebra of continuous functions on the quantum group SU_q(2) is determined as well as centers of other related algebras. Several other results concerning this quantum group are given with direct proofs based on concrete realization of these algebras as algebras of operators on a Hilbert space.

Słowa kluczowe

EN

compact quantum group; center; Haar measure; counit

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2016
• Tom: Vol 56, No. 2
• Strony: 251--272
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Krajczok J.

• Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw

autor

Sołtan P.

• Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw

Bibliografia

• [1] E. Bédos, G. J. Murphy, and L. Tuset, Co-amenability of compact quantum groups, J. Geom. Phys. 40 (2001), no. 2,130-153, DOI 10.1016/S0393-0440(01)00024-9.
• [2] K. R. Davidson, C* -algebras by Example, Fields Institute Monographs, vol. 6, American Mathematical Sociaty, Providence, R.1.1968, DOI 10.1090/fim/006.
• [3] D. Kyed and P. M. Soitan, Property (T) and exotic quantum group norms, J. Noncommut. Geom. 6 (2012), no. 4, 773-800, DOI 10.4171/JNCG/105.
• [4] E. C. Lance, An explicit description of the fundamental unitary for SU (2)q, Comm. Math. Phys. 164 (1994), no. 1, 1-15.
• [5] S. Neshveyev and L. Tuset, Compact Quantum Groups and their Representation Categories, Vol. 20, Société Mathématique de France, Paris 2013, Cours Spécialisés.
• [6] W Rudin, Functional Analysis, New York, Düsseldorf, Johannesburg 1973.
• [7] P. M. Soitan, Quantum SO(3) groups and quantum group actions on M2, J. Noncommut. Geom. 4 (2010), no. 1, 1-28, DOI 10.4171/JNCG/48.
• [8] Ş. Strâtilâ and L. Zsido, Lectures on von Neumann Algebras, Editura Academiei, Bucharest; Abacus Press, Tunbridge Wells, 1979; revision of the 1975 original, translated from the Romanian by Silviu Teleman.
• [9] S. L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), no. 4, 613-665.
• [10] S. L. Woronowicz, Twisted SU(2) group. An example of a noncommutative differential calculus, Publ. Res. Inst. Math. Sci. 23 (1987), no. 1,117-181, DOI 10.2977/prims/1195176848.
• [11] S. L. Woronowicz, Quantum SU(2) and E(2) groups. Contraction procedure, Comm. Math. Phys. 149 (1992), no. 3, 637-652.
• [12] S. L. Woronowicz, Compact quantum groups, Symétries quantiques (Les Houches, 1995), North-Holland, Amsterdam, 1998, 845-884.
• [13] S. L. Woronowicz, Quantum exponential function, Rev. Math. Phys. 12 (2000), no. 6, 873-920, DOI 10.1142/S0129055X00000344.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).