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- Title
On Lie algebra decompositions related to spherical homogeneous spaces.
- Authors
Akhiezer, Dmitri
- Abstract
Let G be a connected, reductive, linear algebraic group over an algebraically closed field k of characteristik zero. Let H and H be two spherical subgroups of G. It is shown that for all g in a Zariski open subset of G one has a Lie algebra decomposition g = h + Ad g ⋅ h, where a is the Lie algebra of a torus and dim a ≤ min (rank G/ H ,rank G/ H ). As an application one obtains an estimate of the transcendence degree of the field k( G/ H x G/ H ) for the diagonal action of G. If k = ℂ and G is a real form of G defined by an antiholomorphic involution σ : G→ G then for a spherical subgroup H ⊂ G and for all g in a Hausdorff open subset of G one has a decomposition g = g + a Ad g ⋅ h, where a is the Lie algebra of σ-invariant torus and dim a ≤ rank G/ H.
- Publication
Manuscripta Mathematica, 1993, Vol 80, Issue 1, p81
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/BF03026538