Browsing by Subject "Invariant theory"
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Item Open Access Degree bounds for modular covariants(De Gruyter, 2020) Elmer, J.; Sezer, MüfitLet V, W be representations of a cyclic group G of prime order p over a field k of characteristic p. The module of covariants k[V, W]G is the set of G-equivariant polynomial maps V → W, and is a module over k[V ]G. We give a formula for the Noether bound β(k[V, W]G, k[V ]G), i.e. the minimal degree d such that k[V, W]G is generated over k[V ]G by elements of degree at most dItem Open Access Degree of reductivity of a modular representation(World Scientific Publishing, 2017) Kohls, M.; Sezer, M.For a finite-dimensional representation V of a group G over a field F, the degree of reductivity δ(G,V) is the smallest degree d such that every nonzero fixed point υ ∈ VG/{0} can be separated from zero by a homogeneous invariant of degree at most d. We compute δ(G,V) explicitly for several classes of modular groups and representations. We also demonstrate that the maximal size of a cyclic subgroup is a sharp lower bound for this number in the case of modular abelian p-groups. © 2017 World Scientific Publishing Company.Item Open Access A note on the Hilbert ideals of a cyclic group of prime order(Academic Press, 2007) Sezer, M.The Hilbert ideal is the ideal generated by positive degree invariant polynomials of a finite group. For a cyclic group of prime order p, we show that the image of the transfer lie in the ideal generated by invariants of degree at most p - 1. Consequently we show that the Hilbert ideal corresponding to an indecomposable representation is generated by polynomials of degree at most p, confirming a conjecture of Harm Derksen and Gregor Kemper for this case. © 2007 Elsevier Inc. All rights reserved.Item Open Access Vector invariants of permutation groups in characteristic zero(World Scientific Publishing Co. Pte. Ltd., 2023-12-21) Reimers, F.; Sezer, MüfitWe consider a finite permutation group acting naturally on a vector space V over a field k. A well-known theorem of G¨obel asserts that the corresponding ring of invariants k[V ] G is generated by the invariants of degree at most `dim V 2 ´ . In this paper, we show that if the characteristic of k is zero, then the top degree of vector coinvariants k[V m]G is also bounded above by `dim V 2 ´ , which implies the degree bound `dim V 2 ´ + 1 for the ring of vector invariants k[V m] G. So, G¨obel’s bound almost holds for vector invariants in characteristic zero as well.