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Comptes Rendus Mathématique
Volume 346, n° 3-4
pages 193-198 (février 2008)
Doi : 10.1016/j.crma.2007.12.012
Received : 17 September 2007 ;  accepted : 9 December 2007
Modular classes of Loday algebroids
Algébroïdes de Loday
 

Mathieu Stiénon a, 1 , Ping Xu b, 2
a Departement Mathematik, Eidgenössische Technische Hochschule Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland 
b Department of Mathematics, Pennsylvania State University, 109, McAllister Building, University Park, PA 16802, USA 

Abstract

We introduce the concept of Loday algebroids, a generalization of Courant algebroids. We define the naive cohomology and modular class of a Loday algebroid, and we show that the modular class of the double of a Lie bialgebroid vanishes. For Courant algebroids, we describe the relation between the naive and standard cohomologies and we conjecture that they are isomorphic when the Courant algebroid is transitive. To cite this article: M. Stiénon, P. Xu, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

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Résumé

Nous introduisons le concept d’algébroïde de Loday, une généralisation des algébroïdes de Courant, en définissons la cohomologie naïve et la classe modulaire, et nous montrons que la classe modulaire du double d’un bigébroïde de Lie est nulle. Dans le cas des algébroïdes de Courant, nous décrivons la relation entre les cohomologies naïve et standard et nous conjecturons qu’elles sont isomorphes quand l’algébroïde de Courant est transitif. Pour citer cet article : M. Stiénon, P. Xu, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.
1  Research supported by the European Union through the FP6 Marie Curie R.T.N. ENIGMA (Contract number MRTN-CT-2004-5652).
2  Research partially supported by NSF grant DMS-0605725 & NSA grant H98230-06-1-0047.


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