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Invariant Ideals and Matsushima's Criterion

Ivan V. Arzhantsev
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Abstract

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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Ivan V. Arzhantsev. 2005-06-21. Invariant Ideals and Matsushima's Criterion. https://arxiv.org/abs/math/0506430

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