Geodesic
Drinfel’d doubles and Ehresmann doubles for Lie algebroids and Lie bialgebroids
Mackenzie, K.1
1 School of Mathematics and Statistics, University of Sheffield, Sheffield, S3 7RH, England
Electronic research announcements of the American Mathematical Society, Tome 04 (1998), pp. 74-87.

Voir la notice de l'article provenant de la source American Mathematical Society

We show that the Manin triple characterization of Lie bialgebras in terms of the Drinfel’d double may be extended to arbitrary Poisson manifolds and indeed Lie bialgebroids by using double cotangent bundles, rather than the direct sum structures (Courant algebroids) utilized for similar purposes by Liu, Weinstein and Xu. This is achieved in terms of an abstract notion of double Lie algebroid (where “double” is now used in the Ehresmann sense) which unifies many iterated constructions in differential geometry.
DOI : 10.1090/S1079-6762-98-00050-X

Mackenzie, K. 1

1 School of Mathematics and Statistics, University of Sheffield, Sheffield, S3 7RH, England 
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Mackenzie, K. Drinfel’d doubles and Ehresmann doubles for Lie algebroids and Lie bialgebroids. Electronic research announcements of the American Mathematical Society, Tome 04 (1998), pp. 74-87. doi : 10.1090/S1079-6762-98-00050-X. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-98-00050-X/

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