TY - JOUR
T1 - The separating variety for the basic representations of the additive group
AU - Dufresne, Emilie
AU - Kohls, Martin
PY - 2013/3/1
Y1 - 2013/3/1
N2 - 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 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.
AB - 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 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.
KW - Basic actions
KW - Invariant theory
KW - Locally nilpotent derivations
KW - Separating invariants
KW - Weitzenböck derivations
UR - http://www.scopus.com/inward/record.url?scp=84871963053&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2012.11.043
DO - 10.1016/j.jalgebra.2012.11.043
M3 - Article
AN - SCOPUS:84871963053
SN - 0021-8693
VL - 377
SP - 269
EP - 280
JO - Journal of Algebra
JF - Journal of Algebra
ER -