The Groups of Basic Automorphisms of Complete Cartan Foliations
- Authors: Sheina K.I.1, Zhukova N.I.1
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Affiliations:
- Department of Informatics, Mathematics and Computer Sciences
- Issue: Vol 39, No 2 (2018)
- Pages: 271-280
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/201657
- DOI: https://doi.org/10.1134/S1995080218020245
- ID: 201657
Cite item
Abstract
For a complete Cartan foliation (M,F) we introduce two algebraic invariants g0(M,F) and g1(M,F) which we call structure Lie algebras. If the transverse Cartan geometry of (M,F) is effective then g0(M,F) = g1(M,F). Weprove that if g0(M,F) is zero then in the category of Cartan foliations the group of all basic automorphisms of the foliation (M,F) admits a unique structure of a finite-dimensional Lie group. In particular, we obtain sufficient conditions for this group to be discrete. We give some exact (i.e. best possible) estimates of the dimension of this group depending on the transverse geometry and topology of leaves. We construct several examples of groups of all basic automorphisms of complete Cartan foliations.
About the authors
K. I. Sheina
Department of Informatics, Mathematics and Computer Sciences
Author for correspondence.
Email: ksheina@hse.ru
Russian Federation, ul. Myasnitskaya 20, Moscow, 101000
N. I. Zhukova
Department of Informatics, Mathematics and Computer Sciences
Email: ksheina@hse.ru
Russian Federation, ul. Myasnitskaya 20, Moscow, 101000