On the structure of real transitive lie algebras

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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 T associated to L. We relate those chain decompositions of T which result from considering T-invariant foliations to Jordan-Holder sequences (in the sense of Cartan and Guillemin) for L. Local coordinates are constructed which display the nature of the partial differential equations defining T; in particular, locally homogeneous pseudocomplex structures (also called CR-structures) are associated to the nonabelian quotients of complex type in a Jordan-Holder sequence for L.

Original languageEnglish (US)
Pages (from-to)1-71
Number of pages71
JournalTransactions of the American Mathematical Society
Volume286
Issue number1
DOIs
StatePublished - 1984

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