Algorithmic invariant theory of nonreductive groups
Let \(X\) be an affine variety over the algebraically closed field \(K\) and \(G\) a linear algebraic group over \(K\) acting on \(X\). The paper gives a survey of algorithms in invariant theory with an emphasis on nonreductive groups. A new method for computing the ring of invariants \(K[X]^G\) is presented. It is assumed that the invariant field \(K(X)^G\) is equal to the field of fractions of \(K[X]^G\). This is satisfied for unipotent groups. There is also a new result on separating invariants. There exists a separating set of invariants of size and most \(2\cdot\dim(K[X]^G)+1\). Here a subset \(S\subseteq K[X]^G\) is called separating, if the following condition holds for all points \(p, q\in X:\) If there exists \(f\in K[X]^G\) with \(f(p)\neq f(q)\), then there exists \(g\in S\) with \(g(p)\neq g(q)\).
scientific article; zbMATH DE number 6134567
scientific article