The separating variety for the basic representations of the additive group
The separating variety for the basic representations of the additive group
复制标题
加法群基本表示的分离式
DOI：
10.1016/j.jalgebra.2012.11.043
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发表时间：
2012
影响因子：
0.9
通讯作者：
M. Kohls
中科院分区：
文献类型：
--
作者：
Emilie Dufresne;M. Kohls
对于作用于仿射簇 X 的群 G，分离簇是 X×X 编码的闭子簇，其中 X 的点由不变量分隔。我们关注特征零域的加法群的不可分解的n+1维有理线性表示Vn，并将分离簇分解为不可约分量的并集。我们证明，如果 n 是奇数、可被四整除或等于二，则具有维度 n+2 的动作图的闭包是分离簇的唯一组成部分。在其余情况下，存在维度为 n+1 的第二个不可约分量。我们得出的结论是，在这些情况下，不存在多项式分离代数。
For a group G acting on an affine variety X, the separating variety is the closed subvariety of X×X encoding which points of X are separated by invariants. We concentrate on the indecomposable rational linear representations Vnof dimension n+1 of the additive group of a field of characteristic zero, and decompose the separating variety into the union of irreducible components. We show that if n is odd, divisible by four, or equal to two, the closure of the graph of the action, which has dimension n+2, is the only component of the separating variety. In the remaining cases, there is a second irreducible component of dimension n+1. We conclude that in these cases, there are no polynomial separating algebras.