The Groups of Basic Automorphisms of Complete Cartan Foliations
- Авторы: Sheina K.1, Zhukova N.1
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Учреждения:
- Department of Informatics, Mathematics and Computer Sciences
- Выпуск: Том 39, № 2 (2018)
- Страницы: 271-280
- Раздел: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/201657
- DOI: https://doi.org/10.1134/S1995080218020245
- ID: 201657
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Аннотация
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.
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Об авторах
K. Sheina
Department of Informatics, Mathematics and Computer Sciences
Автор, ответственный за переписку.
Email: ksheina@hse.ru
Россия, ul. Myasnitskaya 20, Moscow, 101000
N. Zhukova
Department of Informatics, Mathematics and Computer Sciences
Email: ksheina@hse.ru
Россия, ul. Myasnitskaya 20, Moscow, 101000
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