共查询到20条相似文献,搜索用时 3 毫秒
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Let G be an affine algebraic group acting on an affine variety X. We present an algorithm for computing generators of the invariant ring KG[X] 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 KG[X] in terms of a so-called colon-operation. From this, generators of KG[X] 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 KG[X]. Along the way, we develop some techniques for dealing with nonfinitely generated algebras. In particular, we introduce the finite generation ideal. 相似文献
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Let V be a Weyl module either for a reductive algebraic group G or for the corresponding quantum group Uq. If G is defined over a field of positive characteristic p, respectively if q is a primitive lth root of unity (in an arbitrary field) then V has a Jantzen filtration V=V0⊃V1⊃?⊃Vr=0. The sum of the positive terms in this filtration satisfies a well-known sum formula.If T denotes a tilting module either for G or Uq then we can similarly filter the space HomG(V,T), respectively HomUq(V,T) and there is a sum formula for the positive terms here as well.We give an easy and unified proof of these two (equivalent) sum formulas. Our approach is based on an Euler type identity which we show holds without any restrictions on p or l. In particular, we get rid of previous such restrictions in the tilting module case. 相似文献
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Let G be an affine algebraic group and let X be an affine algebraic variety. An action G × X → X is called observable if for any G-invariant, proper, closed subset Y of X there is a nonzero invariant f ∈
\Bbbk\Bbbk [X]
G
such that f|
Y
= 0. We characterize this condition geometrically as follows. The action G × X → X is observable if and only if:
相似文献
(1) the action is stable, that is there exists a nonempty open subset U ⊆ X consisting of closed orbits; and | |
(2) the field \Bbbk\Bbbk(X) G of G-invariant rational functions on X is equal to the quotient field of \Bbbk\Bbbk[X] G . |
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Jörg Winkelmann 《Transformation Groups》2009,14(2):483-491
We generalize a construction of Freudenburg and Moser-Jauslin in order to obtain an example of a nonlinearizable action of
a commutative reductive group on the affine space for every field k of characteristic zero which admits a quadratic extension.
Supported by DFG Forschergruppe 790. 相似文献
6.
Franz-Viktor Kuhlmann 《Advances in Mathematics》2004,188(2):399-424
We consider the Zariski space of all places of an algebraic function field F|K of arbitrary characteristic and investigate its structure by means of its patch topology. We show that certain sets of places with nice properties (e.g., prime divisors, places of maximal rank, zero-dimensional discrete places) lie dense in this topology. Further, we give several equivalent characterizations of fields that are large, in the sense of F. Pop's Annals paper Embedding problems over large fields. We also study the question whether a field K is existentially closed in an extension field L if L admits a K-rational place. In the appendix, we prove the fact that the Zariski space with the Zariski topology is quasi-compact and that it is a spectral space. 相似文献
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Gopal Prasad Andrei S. Rapinchuk 《Proceedings of the American Mathematical Society》2002,130(8):2219-2227
We prove that for a reductive algebraic group over an infinite field the group of rational points does not contain any noncentral finitely generated normal subgroups.
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Siddhartha Bhattacharya 《Transactions of the American Mathematical Society》2004,356(12):4687-4700
We study endomorphism actions of a discrete semigroup on a connected group . We give a necessary and sufficient condition for expansiveness of such actions provided is either a Lie group or a solenoid.
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This paper gives an algorithm for computing invariant rings of reductive groups in arbitrary characteristic. Previously, only
algorithms for linearly reductive groups and for finite groups have been known. The key step is to find a separating set of
invariants. 相似文献
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We study the K-theory of actions of diagonalizable group schemes on noetherian regular separated algebraic spaces: our main result shows how to reconstruct the K-theory ring of such an action from the K-theory rings of the loci where the stabilizers have constant dimension. We apply this to the calculation of the equivariant K-theory of toric varieties, and give conditions under which the Merkurjev spectral sequence degenerates, so that the equivariant K-theory ring determines the ordinary K-theory ring. We also prove a very refined localization theorem for actions of this type. Mathematics Subject Classification (2000) 19E08, 14L30 相似文献
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Publications mathématiques de l'IHÉS - 相似文献
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We analyze the structure of a large class of connected algebraic rings over an algebraically closed field of positive characteristic using Greenberg’s perfectization functor. We then give applications to rigidity problems for representations of Chevalley groups. 相似文献
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Let A and G be finite groups of relatively prime orders and assume that A acts on G via automorphisms. We study how certain conditions on G imply its solvability when we assume the existence of a unique A-invariant Sylow p-subgroup for p equal to 2 or 3. 相似文献