no. 1
Homology and modular classes of Lie algebroids
[Classes d’homologie et classes modulaire pour les algébroïdes de Lie]
Grabowski, Janusz1 ; Marmo, Giuseppe2 ; Michor, Peter W.3
1 Polish Academy of Sciences Mathematical Institute Śniadeckich 8, P.O. Box 21 00-956 Warszawa (Poland)
2 Universitá di Napoli Federico II and INFN, Dipartimento di Scienze Fisice Sezione di Napoli, via Cintia 80126 Napoli (Italy)
3 Universität Wien Institut für Mathematik Nordbergstrasse 15 A-1090 Wien (Austria) and Erwin Schrödinger Institut für Mathematische Physik Boltzmanngasse 9 A-1090 Wien (Austria)
Annales de l'Institut Fourier, Tome 56 (2006) no. 1, pp. 69-83.

Pour un algébroïde de Lie, le choix des divergences à la mode classique donne une théorie de l’homologie unique. Elles définissent aussi naturellement les classes modulaires de quelques morphismes des algébroïdes de Lie. Cette méthode, appliquée à l’application d’ancre, nous permet de retrouver la classe modulaire due à S. Evens, J.-H. Lu, et A. Weinstein.

For a Lie algebroid, divergences chosen in a classical way lead to a uniquely defined homology theory. They define also, in a natural way, modular classes of certain Lie algebroid morphisms. This approach, applied for the anchor map, recovers the concept of modular class due to S. Evens, J.-H. Lu, and A. Weinstein.

DOI : 10.5802/aif.2172
Classification : 17B56, 17B66, 17B70, 53C05
Keywords: Lie algebroid, de Rham cohomology, Poincaré duality, divergence
Mot clés : algébroïde de Lie, cohomologie de de Rham, dualité de Poincaré, divergence
Grabowski, Janusz 1 ; Marmo, Giuseppe 2 ; Michor, Peter W. 3

1 Polish Academy of Sciences Mathematical Institute Śniadeckich 8, P.O. Box 21 00-956 Warszawa (Poland)
2 Universitá di Napoli Federico II and INFN, Dipartimento di Scienze Fisice Sezione di Napoli, via Cintia 80126 Napoli (Italy)
3 Universität Wien Institut für Mathematik Nordbergstrasse 15 A-1090 Wien (Austria) and Erwin Schrödinger Institut für Mathematische Physik Boltzmanngasse 9 A-1090 Wien (Austria) 
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Grabowski, Janusz; Marmo, Giuseppe; Michor, Peter W. Homology and modular classes of Lie algebroids. Annales de l'Institut Fourier, Tome 56 (2006) no. 1, pp. 69-83. doi : 10.5802/aif.2172. http://www.numdam.org/articles/10.5802/aif.2172/

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