Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 103, 40 pages      arXiv:0911.3344      https://doi.org/10.3842/SIGMA.2009.103
Contribution to the Special Issue “Élie Cartan and Differential Geometry”

Isomorphism of Intransitive Linear Lie Equations

Jose Miguel Martins Veloso
Faculdade de Matematica, UFPA, Belem, PA, CEP 66075-110, Brasil

Received February 09, 2009, in final form November 11, 2009; Published online November 17, 2009

Abstract
We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an intransitive Lie algebra with each intransitive linear Lie equation, and from the intransitive Lie algebra we recover the linear Lie equation, unless of formal isomorphism. The intransitive Lie algebra gives the structure functions introduced by É. Cartan.

Key words: Lie equations; Lie groupoids; intransitive; isomorphism.

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