TY - JOUR

T1 - Using extended Derksen ideals in computational invariant theory

AU - Kemper, Gregor

N1 - Publisher Copyright:
© 2015 .

PY - 2016/1/1

Y1 - 2016/1/1

N2 - This paper contains three new algorithms for computing invariant rings. The first two apply to invariants of a finite group acting on a finitely generated algebra over a Euclidean ring. This may be viewed as a first step in "computational arithmetic invariant theory." As a special case, the algorithms can compute multiplicative invariant rings. The third algorithm computes the invariant ring of a reductive group acting on a vector space, and often performs better than the algorithms known to date.The main tool upon which two of the algorithms are built is a generalized version of an ideal that was already used by Derksen in his algorithm for computing invariants of linearly reductive groups. As a further application, these so-called extended Derksen ideals give rise to invariantization maps, which turn an arbitrary ring element into an invariant.For the most part, the algorithms of this paper have been implemented.

AB - This paper contains three new algorithms for computing invariant rings. The first two apply to invariants of a finite group acting on a finitely generated algebra over a Euclidean ring. This may be viewed as a first step in "computational arithmetic invariant theory." As a special case, the algorithms can compute multiplicative invariant rings. The third algorithm computes the invariant ring of a reductive group acting on a vector space, and often performs better than the algorithms known to date.The main tool upon which two of the algorithms are built is a generalized version of an ideal that was already used by Derksen in his algorithm for computing invariants of linearly reductive groups. As a further application, these so-called extended Derksen ideals give rise to invariantization maps, which turn an arbitrary ring element into an invariant.For the most part, the algorithms of this paper have been implemented.

KW - Algorithmic invariant theory

KW - Arithmetic invariant theory

KW - Invariantization

KW - Multiplicative invariant theory

UR - http://www.scopus.com/inward/record.url?scp=84937526986&partnerID=8YFLogxK

U2 - 10.1016/j.jsc.2015.02.004

DO - 10.1016/j.jsc.2015.02.004

M3 - Article

AN - SCOPUS:84937526986

SN - 0747-7171

VL - 72

SP - 161

EP - 181

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

ER -