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Invariant intrinsic Finsler metrics on homogeneous spaces and strong subalgebras of Lie algebras

Authors
  • Gorbatsevich, V. V.1
  • 1 Moscow State Technological University, Moscow, Russia , Moscow (Russia)
Type
Published Article
Journal
Siberian Mathematical Journal
Publisher
Springer US
Publication Date
Jan 01, 2008
Volume
49
Issue
1
Pages
36–47
Identifiers
DOI: 10.1007/s11202-008-0004-1
Source
Springer Nature
Keywords
License
Yellow

Abstract

We study the algebraic conditions for all intrinsic metrics to be Finsler on a homogeneous space. These conditions were firstly found by BerestovskiÄ­ in terms of Lie algebras and their subalgebras (the corresponding subalgebras will be called strong). We obtain a description of the structure of strong subalgebras in semisimple solvable Lie algebras as well as Lie algebras of a general form. We also obtain some results on maximal strong subalgebras and Lie algebras with at least one strong subalgebra.

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