Invariant Ideals and Matsushima's Criterion

Details Invariant Ideals and Matsushima's Criterion Invariant Ideals and Matsushima's Criterion

2005-06-21

arxiv.org/abs/math/0506430v1

Comm. Algebra 36 (2008), no. 12, 4368--4374

Mathematics

Algebraic Geometry

6 pages

Scientific paper

Let G be a reductive algebraic group and H a closed subgroup of G. Explicit
constructions of G-invariant ideals in the algebra K[G/H] are given. This
allows to obtain an elementary proof of Matsushima's criterion: a homogeneous
space G/H is an affine variety if and only if H is reductive.

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