Computing invariants of algebraic groups in arbitrary characteristic

• Autores: Harm Derksen, Gregor Kemper
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 217, Nº 5, 2008, págs. 2089-2129
• Idioma: inglés
• DOI: 10.1016/j.aim.2007.08.016
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• Resumen

  • Let G be an affine algebraic group acting on an affine variety X. We present an algorithm for computing generators of the invariant ring K[X]G in the case where G is reductive. Furthermore, we address the case where G is connected and unipotent, so the invariant ring need not be finitely generated. For this case, we develop an algorithm which computes K[X]G in terms of a so-called colon-operation. From this, generators of K[X]G can be obtained in finite time if it is finitely generated. Under the additional hypothesis that K[X] is factorial, we present an algorithm that finds a quasi-affine variety whose coordinate ring is K[X]G. Along the way, we develop some techniques for dealing with nonfinitely generated algebras. In particular, we introduce the finite generation ideal