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Bichon, Julien; Kyed, David; Raum, Sven. Higher l 2-Betti Numbers of Universal Quantum Groups. Canadian mathematical bulletin, Tome 61 (2018) no. 2, pp. 225-235. doi: 10.4153/CMB-2017-036-3
@article{10_4153_CMB_2017_036_3,
author = {Bichon, Julien and Kyed, David and Raum, Sven},
title = {Higher l {2-Betti} {Numbers} of {Universal} {Quantum} {Groups}},
journal = {Canadian mathematical bulletin},
pages = {225--235},
year = {2018},
volume = {61},
number = {2},
doi = {10.4153/CMB-2017-036-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-036-3/}
}
TY - JOUR AU - Bichon, Julien AU - Kyed, David AU - Raum, Sven TI - Higher l 2-Betti Numbers of Universal Quantum Groups JO - Canadian mathematical bulletin PY - 2018 SP - 225 EP - 235 VL - 61 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-036-3/ DO - 10.4153/CMB-2017-036-3 ID - 10_4153_CMB_2017_036_3 ER -
%0 Journal Article %A Bichon, Julien %A Kyed, David %A Raum, Sven %T Higher l 2-Betti Numbers of Universal Quantum Groups %J Canadian mathematical bulletin %D 2018 %P 225-235 %V 61 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-036-3/ %R 10.4153/CMB-2017-036-3 %F 10_4153_CMB_2017_036_3
[Ban97a] [Ban97a] Banica, T., Legroupe quantique compact libre U(n). Comm. Math. Phys. 190(1997), no. 1, 143–172. http://dx.doi.Org/10.1007/s002200050237 Google Scholar
[BS09] [BS09] Banica, T. and Speicher, R., Liberation orthogonal Lie groups. Adv. Math. 222(2009), no. 4, 1461–1501. http://dx.doi.Org/10.1016/j.aim.2009.06.009 Google Scholar
[BV10] [BV10] Banica, T. and Vergnioux, R., Invariants ofthe half-liberated orthogonal group. Ann. Inst. Fourier 60(2010), no. 6, 2137–2164. Google Scholar | DOI
[BMT01] [BMT01] Bédos, E., Murphy, G. J., and Tuset, L., Co-amenability of compact quantum groups. J. Geom. Phys. 40(2001), no. 2, 130–153. Google Scholar | DOI
[vdB98] [vdB98] van den Bergh, M., A relation between Hochschild homology and cohomology for Gorenstei rings. Proc. Amer. Math. Soc. 126(1998), no. 5,1345–1348. Google Scholar | DOI
[BDD11] [BDD11] Bhowmick, J., D'Andrea, F., and Dabrowski, L., Quantum isometries ofthe finite noncommutative geometry of the Standard model. Comm. Math. Phys. 307(2011), 101–131. http://dx.doi.Org/10.1007/s00220-011-1301-2 Google Scholar
[Bicl6] [Bicl6] Bichon, J., Cohomological dimensions of universal cosoverign Hopf algebras. Publicacions Matemàtiques, to appear. arxiv:1611.02069 Google Scholar
[BNY15] [BNY15] Bichon, J., Neshveyev, S., and Yamashita, M., Graded twisting of categories and quantum groups by group actions. Ann. Inst. Fourier 66(2016), no. 6, 2299–2338. Google Scholar | DOI
[BNY16] [BNY16] Bichon, J., Neshveyev, S., and Yamashita, M., Graded twisting of comodule algebras and module categories. arxiv:1 604.02078 Google Scholar
[Bral2] [Bral2] Brannan, M., Approximation properties for free orthogonal andfree unitary quantum groups. J. Reine Angew. Math. 672(2012), 223–251. Google Scholar
[Chil4] [Chil4] Chirvasitu, A., Cosemisimple Hopf algebras are faithfully flat over Hopf subalgebras. Algebra Number Theory 8(2014), no. 5,1179–1199. http://dx.doi.Org/10.214O/ant.2O14.8.1179 Google Scholar
[CHT09] [CHT09] Collins, B., Härtel, Johannes, and Thom, A., Homology offree quantum groups. C. R. Math. Acad. Sei. Paris 347(2009), no. 5-6, 271–276. http://dx.doi.Org/10.1016/j.crma.2009.01.021 Google Scholar
[FimlO] [FimlO] Fima, P. Kazhdan's property T for discrete quantum groups. Internat. J. Math. 221(2010), no. 1, 47–65. http://dx.doi.Org/10.1142/S0129167X1000591X Google Scholar
[KVOO] [KVOO] Kustermans, J. and Vaes, S., Locally compact quantum groups. Ann. Sei. École Norm. Sup. (4) 33(2000), no. 6, 837–934. http://dx.doi.Org/10.1016/S0012-9593(00)01055-7 Google Scholar
[KyeO8a] [KyeO8a] Kyed, D., L2-Betti numbers of coamenable quantum groups. Münster J. Math. 1(2008), 143–179. Google Scholar
[KyeO8b] [KyeO8b] Kyed, D., L2-homology for compact quantum groups. Math. Scand. 103(2008), no. 1,111–129. Google Scholar | DOI
[Kyell] [Kyell] Kyed, D., On the zeroth L2-homology of a quantum group. Münster J. Math. 4(2011), 119–127. Google Scholar
[Kyel2] [Kyel2] Kyed, D., An L2-Kunneth formula for tracial algebras. J. Operator Theory 67(2012), 317–327. Google Scholar
[KR16] [KR16] Kyed, D. and Raum, S., On the l2-Betti numbers of universal quantum groups. Math. Ann., to appear. arxiv:1 610.05474 Google Scholar
[LücO2] [LücO2] Lück, W., L2-invariants: theory and applications to geometry and K-theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, 44, Folge, A Series of Modern Surveys in Mathematics, Springer-Verlag, Berlin, 2002. Google Scholar
[MN06] [MN06] Meyer, R. and Nest, R., The Baum-Connes conjeeture via localisation of categories. Topology 45(2006), no. 2, 209–259. http://dx.doi.Org/10.1016/j.top.2005.07.001 Google Scholar
[ReiOl] [ReiOl] Reich, H., On the K-and L-theory ofthe algebra of Operators affiliated to a finite von Neumann algebra. Jf-Theory 24, no. 4, 303–326. http://dx.doi.Org/10.1023/A:1014078228859 Google Scholar
[SauO2] [SauO2] Sauer, R., L2-invariants of groups and discrete measured groupoids. Ph.D. Dissertation, University of Münster, 2002. Google Scholar
[Tho08] [Tho08] Thom, A., L2 *-cohomology for von Neumann algebras. Geom. Funct. Anal. 18(2008), no. 1, 251–270. Google Scholar | DOI
[VW96] [VW96] Van Daele, A. and Wang, S., Universal quantum groups. Internat. J. Math. 7(1996), no. 2, 255–263. http://dx.doi.Org/10.1142/S0129167X96000153 Google Scholar
[VerO7] [VerO7] Vergnioux, R., The property of rapid decayfor discrete quantum groups. J. Operator Theory 57(2007), 303–324. Google Scholar
[Verl2] [Verl2] Vergnioux, R., Paths in quantum Cayley trees and L2-cohomology. Adv. Math. 229(2012), 2686–2711. http://dx.doi.Org/10.1016/j.aim.2O12.01.011 Google Scholar
[Voill] [Voill] Voigt, C., The Baum-Connes conjeeture for free orthogonal quantum groups. Adv. Math. 227(2011), no. 5, 1873–1913. http://dx.doi.Org/10.1016/j.aim.2O11.04.008 Google Scholar
[Wan95] [Wan95] Wang, S., Free produets ofcompact quantum groups. Comm. Math. Phys. 167(1995), no. 3, 671–692. http://dx.doi.Org/10.1007/BF02101540 Google Scholar
[Wan98] [Wan98] Wang, S., Quantum symmetry groups of finite Spaces. Comm. Math. Phys. 195(1998), 195–211. Google Scholar | DOI
[Wei94] [Wei94] Weibel, C. A., An introduction to homological algebra. Cambridge Studies in Advanced Mathematics, 38, Cambridge University Press, Cambridge, 1994. http://dx.doi.Org/10.1017/CBO9781139644136 Google Scholar
[Wor87] [Wor87] Woronowicz, S. L., Twisted SU(2) group. An example ofa noncommutative differential calculus. Publ. Res. Inst. Math. Sei. 23(1987), 117–181. Google Scholar | DOI
[Wor98] [Wor98] Woronowicz, S. L., Compact quantum groups. In: Symetries quantiques (Les Houches, 1995), North-Holland, Amsterdam, 1998, pp. 845–884. Google Scholar
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