Differential Geometry
Modular classes of Loday algebroids
Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 193-198.

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.

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.

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DOI: 10.1016/j.crma.2007.12.012
Stiénon, Mathieu 1; Xu, Ping 2

1 Departement Mathematik, Eidgenössische Technische Hochschule Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland
2 Department of Mathematics, Pennsylvania State University, 109, McAllister Building, University Park, PA 16802, USA
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Stiénon, Mathieu; Xu, Ping. Modular classes of Loday algebroids. Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 193-198. doi : 10.1016/j.crma.2007.12.012. http://www.numdam.org/articles/10.1016/j.crma.2007.12.012/

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