DIRAC ACTIONS AND LU’S LIE ALGEBROID

Poisson actions of Poisson Lie groups have an interesting and rich geometric structure. We will generalize some of this structure to Dirac actions of Dirac Lie groups. Among other things, we extend a result of Jiang-Hua Lu, which states that the cotangent Lie algebroid and the action algebroid for a...

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Bibliographic Details
Published in:Transformation groups 2017-12, Vol.22 (4), p.1081-1124
Main Author: MEINRENKEN, E.
Format: Article
Language:English
Subjects:
Algebra
Classification
Lie Groups
Mathematics
Mathematics and Statistics
Topological Groups
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Summary:Poisson actions of Poisson Lie groups have an interesting and rich geometric structure. We will generalize some of this structure to Dirac actions of Dirac Lie groups. Among other things, we extend a result of Jiang-Hua Lu, which states that the cotangent Lie algebroid and the action algebroid for a Poisson action form a matched pair. We also give a full classification of Dirac actions for which the base manifold is a homogeneous space H/K , obtaining a generalization of Drinfeld’s classification for the Poisson Lie group case.
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-017-9424-y