English

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.

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Cite

@article{arxiv.math/0506430,
  title  = {Invariant Ideals and Matsushima's Criterion},
  author = {Ivan V. Arzhantsev},
  journal= {arXiv preprint arXiv:math/0506430},
  year   = {2009}
}

Comments

6 pages

R2 v1 2026-07-22T17:20:59.429Z