Lifting differential operators from orbit spaces
Lifting differential operators from orbit spaces
复制标题
从轨道空间中提升微分算子
DOI：
10.24033/asens.1714
复制
发表时间：
1995
影响因子：
1.9
通讯作者：
Gerald W. Schwarz
中科院分区：
文献类型：
--
作者：
Gerald W. Schwarz
设X为仿射复代数变体，T>(X)表示X上的代数微分算子的（非交换）代数，则T>(X)有一个按微分阶过滤{^(X)}，相应的梯度grT>(X)是可交换的。现在假设X是光滑的，并且是一个G变量，其中G是一个约化复代数群。设TTX: X - > X//G为商态射。然后我们有一种天然的地图(Ti-x) *: (^ (X)) - > ^ (X / fG)。我们找到了(Tvx)*对所有n是满射的条件，在这种情况下，grD（X//G）是有限生成的。我们推测后者总是正确的。我们也考虑了在Gvector束的截面上微分算子的代数的推广。
Let X be an affine complex algebraic variety, and let T>(X) denote the (non-commutative) algebra of algebraic differential operators on X. Then T>(X) has a filtration {^(X)} by order of differentiation, and the associated graded grT>(X) is commutative. Now assume that X is smooth and a Gvariety, where G is a reductive complex algebraic group. Let TTX : X —> X//G be the quotient morphism. Then we have a natural map (Ti-x)* : (^(X)) —> ^(X/fG). We find conditions under which (Tvx)* is surjective for all n, in which case grD(X//G) is finitely generated. We conjecture that the latter is always true. We also consider generalizations to algebras of differential operators on sections of Gvector bundles.