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Drinfel'd doubles and Ehresmann doubles for Lie algebroids and Lie bialgebroids
Author(s):
K.
C. H.
Mackenzie
Journal:
Electron. Res. Announc. Amer. Math. Soc.
4
(1998),
74-87.
MSC (1991):
Primary 58F05;
Secondary 17B66, 18D05, 22A22, 58H05
Posted:
October 22, 1998
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Abstract:
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.
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Additional Information:
K.
C. H.
Mackenzie
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Sheffield, S3 7RH, England
Email:
K.Mackenzie@sheffield.ac.uk
DOI:
10.1090/S1079-6762-98-00050-X
PII:
S 1079-6762(98)00050-X
Received by editor(s):
July 12, 1998
Posted:
October 22, 1998
Communicated by:
Frances Kirwan
Copyright of article:
Copyright
1998,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article K. C. H. Mackenzie, On symplectic double groupoids and the duality of Poisson groupoids, Internat. J. Math. 10 (1999), 435--456.
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