Journal of Lie Theory

no. 2
Pseudogroups via Pseudoactions: Unifying Local, Global, and Infinitesimal Symmetry
Journal of Lie Theory, Volume 26 (2016) no. 2, pp. 535-565
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.
DOI: 10.5802/jolt.900
Classification: 58H05, 58D19
Keywords: Lie algebroid, pseudogroup, Cartan connection, Lie algebra, pseudoaction 
@article{JOLT_2016_26_2_a7,
     author = {A. D. Blaom},
     title = {Pseudogroups via {Pseudoactions:} {Unifying} {Local,} {Global,} and {Infinitesimal} {Symmetry}},
     journal = {Journal of Lie Theory},
     pages = {535--565},
     year = {2016},
     volume = {26},
     number = {2},
     doi = {10.5802/jolt.900},
     zbl = {1347.58003},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.900/}
}
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A. D. Blaom. Pseudogroups via Pseudoactions: Unifying Local, Global, and Infinitesimal Symmetry. Journal of Lie Theory, Volume 26 (2016) no. 2, pp. 535-565. doi: 10.5802/jolt.900

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