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Transformation Groups

, Volume 22, Issue 4, pp 1081–1124 | Cite as

DIRAC ACTIONS AND LU’S LIE ALGEBROID

  • E. MEINRENKENEmail author
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Abstract

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.

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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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