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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


On the structure of real transitive Lie algebras

Author: Jack F. Conn
Journal: Trans. Amer. Math. Soc. 286 (1984), 1-71
MSC: Primary 58H05; Secondary 17B65, 22E65
MathSciNet review: 756031
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Abstract: In this paper, we examine some of the ways in which abstract algebraic objects in a transitive Lie algebra $ L$ are expressed geometrically in the action of each transitive Lie pseudogroup $ \Gamma $ associated to $ L$. We relate those chain decompositions of $ \Gamma $ which result from considering $ \Gamma $-invariant foliations to Jordan-Hölder sequences (in the sense of Cartan and Guillemin) for $ L$. Local coordinates are constructed which display the nature of the partial differential equations defining $ \Gamma $; in particular, locally homogeneous pseudocomplex structures (also called $ {\text{CR}}$-structures) are associated to the nonabelian quotients of complex type in a Jordan-Hölder sequence for $ L$.

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PII: S 0002-9947(1984)0756031-0
Article copyright: © Copyright 1984 American Mathematical Society