[Modules anti-Yetter–Drinfeld stables]
Nous définissons et étudions une classe de modules enlacés (modules anti-Yetter–Drinfeld stables) qui servent de coefficients pour l'homologie et la cohomologie Hopf-cyclique. En particulier, nous expliquons leurs liens avec les modules de Yetter–Drinfeld et les doublets de Drinfeld. Parmi les sources d'exemples de modules anti-Yetter–Drinfeld stables, nous trouvons des extensions de Hopf–Galois munies d'une version transposée de l'action de Miyashita–Ulbrich.
We define and study a class of entwined modules (stable anti-Yetter–Drinfeld modules) that serve as coefficients for the Hopf-cyclic homology and cohomology. In particular, we explain their relationship with Yetter–Drinfeld modules and Drinfeld doubles. Among sources of examples of stable anti-Yetter–Drinfeld modules, we find Hopf–Galois extensions with a flipped version of the Miyashita–Ulbrich action.
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@article{CRMATH_2004__338_8_587_0,
author = {Hajac, Piotr M. and Khalkhali, Masoud and Rangipour, Bahram and Sommerh\"auser, Yorck},
title = {Stable {anti-Yetter{\textendash}Drinfeld} modules},
journal = {Comptes Rendus. Math\'ematique},
pages = {587--590},
publisher = {Elsevier},
volume = {338},
number = {8},
year = {2004},
doi = {10.1016/j.crma.2003.11.037},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2003.11.037/}
}
TY - JOUR AU - Hajac, Piotr M. AU - Khalkhali, Masoud AU - Rangipour, Bahram AU - Sommerhäuser, Yorck TI - Stable anti-Yetter–Drinfeld modules JO - Comptes Rendus. Mathématique PY - 2004 SP - 587 EP - 590 VL - 338 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2003.11.037/ DO - 10.1016/j.crma.2003.11.037 LA - en ID - CRMATH_2004__338_8_587_0 ER -
%0 Journal Article %A Hajac, Piotr M. %A Khalkhali, Masoud %A Rangipour, Bahram %A Sommerhäuser, Yorck %T Stable anti-Yetter–Drinfeld modules %J Comptes Rendus. Mathématique %D 2004 %P 587-590 %V 338 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2003.11.037/ %R 10.1016/j.crma.2003.11.037 %G en %F CRMATH_2004__338_8_587_0
Hajac, Piotr M.; Khalkhali, Masoud; Rangipour, Bahram; Sommerhäuser, Yorck. Stable anti-Yetter–Drinfeld modules. Comptes Rendus. Mathématique, Tome 338 (2004) no. 8, pp. 587-590. doi : 10.1016/j.crma.2003.11.037. http://www.numdam.org/articles/10.1016/j.crma.2003.11.037/
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