Browse > Article
http://dx.doi.org/10.4134/JKMS.2008.45.2.575

REPRESENTATION AND DUALITY OF UNIMODULAR C*-DISCRETE QUANTUM GROUPS  

Lining, Jiang (DEPARTMENT OF MATHEMATICS BEIJING INSTITUTE OF TECHNOLOGY)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.2, 2008 , pp. 575-585 More about this Journal
Abstract
Suppose that D is a $C^*$-discrete quantum group and $D_0$ a discrete quantum group associated with D. If there exists a continuous action of D on an operator algebra L(H) so that L(H) becomes a D-module algebra, and if the inner product on the Hilbert space H is D-invariant, there is a unique $C^*$-representation $\theta$ of D associated with the action. The fixed-point subspace under the action of D is a Von Neumann algebra, and furthermore, it is the commutant of $\theta$(D) in L(H).
Keywords
discrete quantum group$C^*$-algebra; representation; duality;
Citations & Related Records

Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 2
연도 인용수 순위
1 W. Fulton and J. Harrie, Representation Theory: A First Course, Graduate Texts in Mathematics, 129. Readings in Mathematics. Springer-Verlag, New York, 1991
2 A. Van Daele, Multiplier Hopf algebras, Trans. Amer. Math. Soc. 342 (1994), no. 2, 917-932   DOI   ScienceOn
3 A. Van Daele, Discrete quantum groups, J. Algebra 180 (1996), no. 2, 431-444   DOI   ScienceOn
4 A. Van Daele, An algebraic framework for group duality, Adv. Math. 140 (1998), no. 2, 323-366   DOI   ScienceOn
5 A. Van Daele and Y. H. Zhang, Multiplier Hopf algebras of discrete type, J. Algebra 214 (1999), no. 2, 400-417   DOI   ScienceOn
6 E. G. Effros and Z. J. Ruan, Discrete quantum groups. I. The Haar measure, Internat. J. Math. 5 (1994), no. 5, 681-723   DOI
7 E. Abe, Hopf Algebras, Cambridge Tracts in Mathematics, 74. Cambridge University Press, Cambridge-New York, 1980
8 W. Arveson, An Invitation to C*-Algebras, Graduate Texts in Mathematics, no. 39. Springer-Verlag, New York-Heidelberg, 1976
9 L. N. Jiang, M. Z. Guo, and M. Qian, The duality theory of a finite dimensional discrete quantum group, Proc. Amer. Math. Soc. 132 (2004), no. 12, 3537-3547   DOI   ScienceOn
10 L. N. Jiang and Z. D. Wang, The Schur-Weyl duality between quantum group of type A and Hecke algebra, Adv. Math. (China) 29 (2000), no. 5, 444-456
11 M. Jimbo, A q-analogue of U(gl(N+1)), Hecke algebra, and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), no. 3, 247-252   DOI
12 G. J. Murphy, C*-Algebras and Operator Theory, Academic Press, Inc., Boston, MA, 1990
13 K. Szlachanyi and P. Vecsernyes, Quantum symmetry and braid group statistics in G-spin models, Comm. Math. Phys. 156 (1993), no. 1, 127-168   DOI
14 P. Podles and S. L. Woronowicz, Quantum deformation of Lorentz group, Comm. Math. Phys. 130 (1990), no. 2, 381-431   DOI
15 P. M. Soltan, Quantum Bohr compactification, Illinois J. Math. 49 (2005), no. 4, 1245-1270
16 M. E. Sweedler, Hopf Algebras, Mathematics Lecture Note Series W. A. Benjamin, Inc., New York 1969
17 H. Weyl, The Classical Groups. Their Invariants and Representations., Princeton University Press, Princeton, N.J., 1939
18 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
19 S. L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), no. 4, 613-665   DOI