Rocky Mountain Journal of Mathematics

Multiplier Hopf Algebras Imbedded in Locally Compact Quantum Groups

K. De Commer and A. Van Daele
Source: Rocky Mountain J. Math. Volume 40, Number 4 (2010), 1149-1182.
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.rmjm/1283175793
Digital Object Identifier: doi:10.1216/RMJ-2010-40-4-1149
Zentralblatt MATH identifier: 05779823
Mathematical Reviews number (MathSciNet): MR2718809

References

S. Baaj and S. Vaes, Double crossed products of locally compact quantum groups, J. Institute Math. Jussieu 4 (2005), 135-173.
Mathematical Reviews (MathSciNet): MR2115071
Digital Object Identifier: doi:10.1017/S1474748005000034
E. Bédos, G.J. Murphy and L. Tuset, Co-amenability of compact quantum groups, J. Geom. Phys. 40 (2001), 130-153.
Mathematical Reviews (MathSciNet): MR1862084
Zentralblatt MATH: 1011.46056
L. Delvaux and A. Van Daele, Algebraic quantum hypergroups, Adv. Math., to appear.
B. Drabant, A. Van Daele and Y. Zhang, Actions of multiplier Hopf algebras, Comm. Algebra 27 (1999), 4117-4172.
Mathematical Reviews (MathSciNet): MR1705859
Zentralblatt MATH: 0951.16013
Digital Object Identifier: doi:10.1080/00927879908826688
A. Klimyk and K. Schmudgen, Quantum groups and their representations, Springer, Berlin, 1997.
Mathematical Reviews (MathSciNet): MR1492989
A.W. Knapp, Lie groups, Lie algebras and cohomology, Princeton Univ. Press, Princeton, NJ, 1988.
Mathematical Reviews (MathSciNet): MR938524
Zentralblatt MATH: 0648.22010
J. Kustermans, KMS-weights on C$^*$-algebras, Preprint Odense Universitet (1997), arxiv:math.funct-an/9704008.
--------, One-parameter representations on C$^*$-algebras, Preprint Odense Universitet (1997), arxiv:math.funct-an/9707009.
--------, The analytic structure of an algebraic quantum group, J. Algebra 259 (2003), 415-450.
Mathematical Reviews (MathSciNet): MR1955527
Zentralblatt MATH: 1034.46064
Digital Object Identifier: doi:10.1016/S0021-8693(02)00570-7
J. Kustermans and S. Vaes, Weight theory for $C^*$-algebraic quantum groups, Preprint KU Leuven and University College Cork (1999), arxiv:math.OA/9901063.
Mathematical Reviews (MathSciNet): MR1689849
Zentralblatt MATH: 0957.46037
Digital Object Identifier: doi:10.1016/S0764-4442(99)80288-2
--------, Locally compact quantum groups, Ann. Sci. Ecol. Norm. Sup. 33 (2000), 837-934.
Mathematical Reviews (MathSciNet): MR1832993
Zentralblatt MATH: 1034.46508
Digital Object Identifier: doi:10.1016/S0012-9593(00)01055-7
--------, Locally compact quantum groups in the von Neumann algebra setting, Math. Scand. 92 (2003), 68-92.
Mathematical Reviews (MathSciNet): MR1951446
Zentralblatt MATH: 1034.46067
J. Kustermans and A. Van Daele, C*-algebraic quantum groups arising from algebraic quantum groups, Inter. Jour. Math. 8 (1997), 1067-1139.
Mathematical Reviews (MathSciNet): MR1484867
Zentralblatt MATH: 1009.46038
Digital Object Identifier: doi:10.1142/S0129167X97000500
M.B. Landstad and A. Van Daele, Groups with compact open subgroups and multiplier Hopf $^*$-algebras, Expo. Math. 26 (2008), 197-217.
Mathematical Reviews (MathSciNet): MR2437092
Zentralblatt MATH: 1149.22005
Digital Object Identifier: doi:10.1016/j.exmath.2007.10.004
--------, Compact and discrete subgroups of algebraic quantum groups, K.U. Leuven and University of Trondheim, preprint.
T. Masuda, Y. Nakagami and S.L. Woronowicz, A C$^*$-algebraic framework for quantum groups, Inter. J. Math. 14 (2003), 903-1001.
Mathematical Reviews (MathSciNet): MR2020804
Zentralblatt MATH: 1053.46050
Digital Object Identifier: doi:10.1142/S0129167X03002071
M. Takesaki, Theory of operator algebras II, Springer, Berlin, 2003.
Mathematical Reviews (MathSciNet): MR1943006
Zentralblatt MATH: 1059.46031
S. Vaes, A Radon-Nikodym theorem for von Neumann algebras, J. Operator Theory 46 (2001), 477-489.
Mathematical Reviews (MathSciNet): MR1897150
Zentralblatt MATH: 0995.46042
S. Vaes and A. Van Daele, The Heisenberg commutation relations, commuting squares and the Haar measure on locally compact quantum groups, in Operator algebras and mathematical physics: Conference proceedings, Constanta (Romania), 2001.
A. Van Daele, Multiplier Hopf algebras, Trans. Amer. Math. Soc. 342 (1994), 917-932.
Mathematical Reviews (MathSciNet): MR1220906
Zentralblatt MATH: 0809.16047
Digital Object Identifier: doi:10.2307/2154659
--------, An algebraic framework for group duality, Adv. Math. 140 (1998), 323-366.
Mathematical Reviews (MathSciNet): MR1658585
Zentralblatt MATH: 0933.16043
Digital Object Identifier: doi:10.1006/aima.1998.1775
--------, Quantum groups with invariant integrals, PNAS 97 (2000), 541-556.
Mathematical Reviews (MathSciNet): MR1734954
Zentralblatt MATH: 0984.16038
Digital Object Identifier: doi:10.1073/pnas.97.2.541
--------, The Haar measure on some locally compact quantum groups, arxiv:math.OA /0109004.
--------, Locally compact quantum groups. A von Neumann algebra approach, arxiv:math.OA /0602212.
--------, Discrete quantum groups, J. Algebra 180 (1994), 431-444.
Mathematical Reviews (MathSciNet): MR1378538
Zentralblatt MATH: 0864.17012
Digital Object Identifier: doi:10.1006/jabr.1996.0075
A. Van Daele and Y. Zhang, A survey on multiplier Hopf algebras, %Proc. Conference in in Hopf Algebras and quantum groups, Caenepeel and Van Oystaeyen, eds., %, 269-309. Marcel Dekker, New York, 2000.
Mathematical Reviews (MathSciNet): MR1767620
Zentralblatt MATH: 1020.16032

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Rocky Mountain Journal of Mathematics

Rocky Mountain Journal of Mathematics