The separating variety for the basic representations of the additive group

Details The separating variety for the basic representations of the additive group The separating variety for the basic representations of the additive group

2012-01-28

arxiv.org/abs/1201.5933v1

Mathematics

Commutative Algebra

14 pages

Scientific paper

For a group $G$ acting on an affine variety $X$, the separating variety is the closed subvariety of $X\times X$ encoding which points of $X$ are separated by invariants. We concentrate on the indecomposable rational linear representations $V_n$ of 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.

Affiliated with

Also associated with

No associations

Rating

The separating variety for the basic representations of the additive group does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The separating variety for the basic representations of the additive group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The separating variety for the basic representations of the additive group will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-257346