Comptes Rendus
Stable anti-Yetter–Drinfeld modules
Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 587-590.

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.

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.

Published online:
DOI: 10.1016/j.crma.2003.11.037

Piotr M. Hajac 1, 2; Masoud Khalkhali 3; Bahram Rangipour 3; Yorck Sommerhäuser 4

1 Instytut Matematyczny, Polska Akademia Nauk, ul. Śniadeckich 8, Warszawa, 00-956 Poland
2 Katedra Metod Matematycznych Fizyki, Uniwersytet Warszawski, ul. Hoża 74, Warszawa, 00-682 Poland
3 Department of Mathematics, University of Western Ontario, London ON, Canada
4 Mathematisches Institut, Universität München, Theresienstr. 39, 80333 München, Germany
     author = {Piotr M. Hajac and Masoud Khalkhali and Bahram Rangipour and Yorck Sommerh\"auser},
     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},
AU  - Piotr M. Hajac
AU  - Masoud Khalkhali
AU  - Bahram Rangipour
AU  - Yorck Sommerhäuser
TI  - Stable anti-Yetter–Drinfeld modules
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 587
EP  - 590
VL  - 338
IS  - 8
PB  - Elsevier
DO  - 10.1016/j.crma.2003.11.037
LA  - en
ID  - CRMATH_2004__338_8_587_0
ER  - 
%0 Journal Article
%A Piotr M. Hajac
%A Masoud Khalkhali
%A Bahram Rangipour
%A Yorck Sommerhäuser
%T Stable anti-Yetter–Drinfeld modules
%J Comptes Rendus. Mathématique
%D 2004
%P 587-590
%V 338
%N 8
%I Elsevier
%R 10.1016/j.crma.2003.11.037
%G en
%F CRMATH_2004__338_8_587_0
Piotr M. Hajac; Masoud Khalkhali; Bahram Rangipour; Yorck Sommerhäuser. Stable anti-Yetter–Drinfeld modules. Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 587-590. doi : 10.1016/j.crma.2003.11.037.

[1] T. Brzeziński On modules associated to coalgebra Galois extensions, J. Algebra, Volume 215 (1999), pp. 290-317

[2] S. Caenepeel Brauer Groups, Hopf Algebras and Galois Theory, K-Monographs in Math., vol. 4, Kluwer Academic, Dordrecht, 1998

[3] S. Caenepeel; G. Militaru; S. Zhu Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations, Lecture Notes in Math., vol. 1787, Springer-Verlag, Berlin, 2002

[4] A. Connes; H. Moscovici Cyclic cohomology and Hopf algebra symmetry, Lett. Math. Phys., Volume 52 (2000), pp. 1-28

[5] L. Da̧browski; P.M. Hajac; P. Siniscalco Explicit Hopf–Galois description of SLe2iπ/3(2)-induced Frobenius homomorphisms (D. Kastler; M. Rosso; T. Schucker, eds.), Enlarged Proceedings of the ISI GUCCIA Workshop on Quantum Groups, Noncommutative Geometry and Fundamental Physical Interactions, Nova Science, Commack–New York, 1999, pp. 279-298

[6] Y. Doi; M. Takeuchi Hopf–Galois extensions of algebras, the Miyashita–Ulbrich action, and Azumaya algebras, J. Algebra, Volume 121 (1989), pp. 488-516

[7] P.M. Hajac; M. Khalkhali; B. Rangipour; Y. Sommerhäuser Hopf-cyclic homology and cohomology with coefficients, C. R. Acad. Sci. Paris, Ser. I, Volume 338 (2004)

[8] P. Jara; D. Ştefan Cyclic homology of Hopf Galois extensions and Hopf algebras (Preprint) | arXiv

[9] C. Kassel Quantum Groups, Graduate Texts in Math., vol. 155, Springer-Verlag, Berlin, 1995

[10] M. Khalkhali; B. Rangipour Invariant cyclic homology, K-Theory, Volume 28 (2003), pp. 183-205

[11] B. Pareigis Non-additive ring and module theory II. 𝒞-categories, 𝒞-functors, and 𝒞-morphisms, Publ. Math., Volume 24 (1977), pp. 351-361

Cited by Sources:

Comments - Policy