Invariant Ideals and Matsushima's Criterion
Algebraic Geometry
2009-08-22 v1 Representation Theory
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.
Cite
@article{arxiv.math/0506430,
title = {Invariant Ideals and Matsushima's Criterion},
author = {Ivan V. Arzhantsev},
journal= {arXiv preprint arXiv:math/0506430},
year = {2009}
}
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6 pages