A linear algebraic group is a subgroup of GL(n, k) given as the zero locus of a set of polynomials in the matrix entries. If G is an algebraic group, then g ...
In this paper we review three approaches to this problem. The first one is a straightforward reduction to elimination using Gröbner bases.
impossible. The following example shows that the closure of an orbit of a solvable algebraic group may contain more than one closed orbit which cannot happen.
Jun 9, 2019 · Let O=G.x be the orbit of x∈X. Under which condition do we get that G.¯O⊂¯O? This is apparently true if G is a linear algebraic group ...
Feb 24, 2017 · Theorem 1.12 in Borel's "Linear algebraic groups" tells that there any G affine action could be G-equivariantly closedly embedded in a rational G ...
We consider the problem of deciding whether a given element of the vector space lies in the closure of the orbit of another given element. We describe three ...
Jul 5, 2024 · In this paper we consider a collection of what we call determination problems concerning groups and orbit closures. These problems begin with a ...
Sep 21, 2022 · Theorem. Every orbit of algebraic group action is open in its closure. This yields. Corollary. G · a = G · b ⇐⇒ G · a ⊆ G · b and ...
The orbital decomposition of the closure of an arbitrary orbit in the space of a finite-dimensional linear representation of the group SL(2) is described in ...
The talk is aimed at a discussion of the constructive ways of finding out whether or not O_1 lies in the Zariski closure of O_2.