Invariant Ideals and Matsushima's Criterion [article]

Ivan V. Arzhantsev
2005 arXiv   pre-print
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.
arXiv:math/0506430v1 fatcat:zzcqaxpeqja7db72qxmuchtj4e