Geodesic
A Note on Amenability of Locally Compact Quantum Groups
Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 424-430

Voir la notice de l'article provenant de la source Cambridge University Press

In this short note we introduce a notion called quantum injectivity of locally compact quantum groups, and prove that it is equivalent to amenability of the dual. In particular, this provides a new characterization of amenability of locally compact groups.
DOI : 10.4153/CMB-2012-032-3
Mots-clés : 20G42, 22D25, 46L89, amenability, conditional expectation, injectivity, locally compact quantum group, quantuminjectivity 
Sołtan, Piotr M.; Viselter, Ami. A Note on Amenability of Locally Compact Quantum Groups. Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 424-430. doi: 10.4153/CMB-2012-032-3
@article{10_4153_CMB_2012_032_3,
     author = {So{\l}tan, Piotr M. and Viselter, Ami},
     title = {A {Note} on {Amenability} of {Locally} {Compact} {Quantum} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {424--430},
     year = {2014},
     volume = {57},
     number = {2},
     doi = {10.4153/CMB-2012-032-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-032-3/}
}
TY  - JOUR
AU  - Sołtan, Piotr M.
AU  - Viselter, Ami
TI  - A Note on Amenability of Locally Compact Quantum Groups
JO  - Canadian mathematical bulletin
PY  - 2014
SP  - 424
EP  - 430
VL  - 57
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-032-3/
DO  - 10.4153/CMB-2012-032-3
ID  - 10_4153_CMB_2012_032_3
ER  - 
%0 Journal Article
%A Sołtan, Piotr M.
%A Viselter, Ami
%T A Note on Amenability of Locally Compact Quantum Groups
%J Canadian mathematical bulletin
%D 2014
%P 424-430
%V 57
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-032-3/
%R 10.4153/CMB-2012-032-3
%F 10_4153_CMB_2012_032_3

[1] [1] Bédos, E., Murphy, G. J., and Tuset, L., Amenability and coamenability of algebraic quantum groups. Int. J. Math. Math. Sci. 31 (2002, no. 10, 577–601. Google Scholar | DOI

[2] [2] Bédos, E. and Tuset, L., Amenability and co-amenability for locally compact quantum groups. Internat. J. Math. 14 (2003, no. 8, 865–884. Google Scholar | DOI

[3] [3] Connes, A., Classification of injective factors. Cases II 1; II1; III; 6= 1. Ann. of Math. (2) 104 (1976, no. 1, 73–115. Google Scholar | DOI

[4] [4] Crann, J. and Neufang, M., Quantum group amenability, injectivity, and a question of Bédos–Tuset. arxiv:1208.2986 Google Scholar

[5] [5] Desmedt, P., Quaegebeur, J., and Vaes, S., Amenability and the bicrossed product construction. Illinois J. Math. 46 (2002, no. 4, 1259–1277. Google Scholar

[6] [6] Doplicher, S., Longo, R., Roberts, J. E., and Zsidö, L., A remark on quantum group actions and nuclearity. Rev. Math. Phys. 14 (2002, no. 7-8, 787–796. Google Scholar | DOI

[7] [7] Effros, E. G. and Kishimoto, A., Module maps and Hochschild-Johnson cohomology. Indiana Univ. Math. J. 36 (1987, no. 2, 257–276. Google Scholar | DOI

[8] [8] Enock, M. and Schwartz, J.-M., Algèbres de Kac moyennables. Pacific J. Math. 125 (1986, no. 2, 363–379. http://projecteuclid.org/euclid.pjm/1102700082 Google Scholar

[9] [9] Fima, P., On locally compact quantum groups whose algebras are factors. J. Funct. Anal. 244 (2007, no. 1, 78–94. Google Scholar | DOI

[10] [10] Kustermans, J. and Vaes, S., Locally compact quantum groups. Ann. Sci. E´ cole Norm. Sup. (4) 33 (2000, no. 6, 837–934. Google Scholar | DOI

[11] [11] Kustermans, J. and Vaes, S., Locally compact quantum groups in the von Neumann algebraic setting. Math. Scand. 92 (2003, no. 1, 68–92. Google Scholar

[12] [12] Paterson, A. L. T., Amenability. Mathematical Surveys and Monographs, 29, American Mathematical Society, Providence, RI, 1988. Google Scholar

[13] [13] Ruan, Z.-J., Amenability of Hopf von Neumann algebras and Kac algebras. J. Funct. Anal. 139 (1996, no. 2, 466–499. Google Scholar | DOI

[14] [14] Runde, V., Lectures on amenability. Lecture Notes in Mathematics, 1774, Springer-Verlag, Berlin, 2002. Google Scholar

[15] [15] Runde, V., Characterizations of compact and discrete quantum groups through second duals. J. Operator Theory 60 (2008, no. 2, 415–428. Google Scholar

[16] [16] Sołtan, P. M., Quantum Bohr compactification. Illinois J. Math. 49 (2005, no. 4, 1245–1270. Google Scholar

[17] [17] Takesaki, M., Theory of operator algebras. I. Encyclopaedia of Mathematical Sciences, 124, Operator Algebras and Non-commutative Geometry, 5, Springer-Verlag, Berlin, 2002. [18] R. Tomatsu, Amenable discrete quantum groups. J. Math. Soc. Japan 58 (2006, no. 4, 949–964. Google Scholar | DOI

[19] [19] Woronowicz, S. L., Compact quantum groups. In: Symétries quantiques (Les Houches, 1995), North-Holland, Amsterdam, 1998, pp. 845–884. Google Scholar

Cité par Sources :