Geodesic
Pseudogroups via Pseudoactions: Unifying Local, Global, and Infinitesimal Symmetry
Anthony D. Blaom1
110 Huruhi Road, Waiheke Island 1081, Auckland, New Zealand
Journal of Lie Theory, Tome 26 (2016) no. 2, pp. 535-565

Voir la notice de l'article provenant de la source Heldermann Verlag

A multiplicatively closed, horizontal foliation on a Lie groupoid may be viewed as a "pseudoaction" on the base manifold M. A pseudoaction generates a pseudogroup of transformations of M in the same way an ordinary Lie group action generates a transformation group. Infinitesimalizing a pseudoaction, one obtains the action of a Lie algebra on M, possibly twisted. A global converse to Lie's third theorem proven here states that every twisted Lie algebra action is integrated by a pseudoaction. When the twisted Lie algebra action is complete it integrates to a twisted Lie group action, according to a generalization of Palais' global integrability theorem.
Classification : 58H05, 58D19
Mots-clés : Lie algebroid, pseudogroup, Cartan connection, Lie algebra, pseudoaction

Anthony D. Blaom  1

1 10 Huruhi Road, Waiheke Island 1081, Auckland, New Zealand 
Anthony D. Blaom. Pseudogroups via Pseudoactions: Unifying Local, Global, and Infinitesimal Symmetry. Journal of Lie Theory, Tome 26 (2016) no. 2, pp. 535-565. http://geodesic.mathdoc.fr/item/JOLT_2016_26_2_a7/
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     title = {Pseudogroups via {Pseudoactions:} {Unifying} {Local,} {Global,} and {Infinitesimal} {Symmetry}},
     journal = {Journal of Lie Theory},
     pages = {535--565},
     year = {2016},
     volume = {26},
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     url = {http://geodesic.mathdoc.fr/item/JOLT_2016_26_2_a7/}
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