[Une nouvelle caractérisation des états idempotents sur des groupes quantiques finis ou compacts]
Nous donnons une caractérisation des états idempotents sur un groupe quantique fini en termes des pré-sous-groupes introduits par Baaj, Blanchard, et Skandalis, et en déduisons un isomorphisme entre le réseau des états idempotents et le réseau des sous-algèbres coïdéales d'un groupe quantique fini. Cet isomorphisme s'étend aux groupes quantiques compacts, si on le restreind au sous-algèbres coïdéales expectées.
We show that idempotent states on finite quantum groups correspond to pre-subgroups in the sense of Baaj, Blanchard, and Skandalis. It follows that the lattices formed by the idempotent states on a finite quantum group and by its coidalgebras are isomorphic. We show, furthermore, that these lattices are also isomorphic for compact quantum groups, if one restricts to expected coidalgebras.
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@article{CRMATH_2009__347_17-18_991_0,
author = {Franz, Uwe and Skalski, Adam},
title = {A new characterisation of idempotent states on finite and compact quantum groups},
journal = {Comptes Rendus. Math\'ematique},
pages = {991--996},
publisher = {Elsevier},
volume = {347},
number = {17-18},
year = {2009},
doi = {10.1016/j.crma.2009.06.015},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.crma.2009.06.015/}
}
TY - JOUR AU - Franz, Uwe AU - Skalski, Adam TI - A new characterisation of idempotent states on finite and compact quantum groups JO - Comptes Rendus. Mathématique PY - 2009 SP - 991 EP - 996 VL - 347 IS - 17-18 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2009.06.015/ DO - 10.1016/j.crma.2009.06.015 LA - en ID - CRMATH_2009__347_17-18_991_0 ER -
%0 Journal Article %A Franz, Uwe %A Skalski, Adam %T A new characterisation of idempotent states on finite and compact quantum groups %J Comptes Rendus. Mathématique %D 2009 %P 991-996 %V 347 %N 17-18 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2009.06.015/ %R 10.1016/j.crma.2009.06.015 %G en %F CRMATH_2009__347_17-18_991_0
Franz, Uwe; Skalski, Adam. A new characterisation of idempotent states on finite and compact quantum groups. Comptes Rendus. Mathématique, Tome 347 (2009) no. 17-18, pp. 991-996. doi : 10.1016/j.crma.2009.06.015. https://www.numdam.org/articles/10.1016/j.crma.2009.06.015/
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