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Differential Geometry of Manifolds

2026 №57 (1)

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Di Bartolo A. La Rosa G.

Flag manifolds without one codimensional strata

Pages
39-51
homogeneous spaces Lie algebras codimension two su­bal­gebras simple Lie algebras compact real forms

Abstract

In this paper, we propose a classification of finite-dimensional real Lie algebras that admit subalgebras of codimension two, but no subalgebra of codimension one, which leads to a description of ho­mogeneous spaces without isotropy subgroups of codimension one. This study expands upon the existing body of research on co­dimension-one subalgebras, aiming to extend the analysis to a new setting. The result of this expansion is a comprehensive description of the relevant families. It is demonstrated that a such Lie algebra  contains an ideal , containing the radical of , such that  be­longs to a list , consisting of one compact and two non compact Lie algebras.

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