Invariant Ideals and Matsushima's Criterion
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🧮 math.AG
math.RT
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criterionidealsmatsushimareductiveaffinealgebraalgebraicallows
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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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