Browsing by Subject "Separating invariants"

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    Constructing modular separating invariants
    (2009) Sezer, M.
    We consider a finite dimensional modular representation V of a cyclic group of prime order p. We show that two points in V that are in different orbits can be separated by a homogeneous invariant polynomial that has degree one or p and that involves variables from at most two summands in the dual representation. Simultaneously, we describe an explicit construction for a separating set consisting of polynomials with these properties. © 2009 Elsevier Inc. All rights reserved.
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    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.
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    Explicit separating invariants for cyclic p-groups
    (Elsevier, 2011-02) Sezer, M.
    We consider a finite-dimensional indecomposable modular representation of a cyclic p-group and we give a recursive description of an associated separating set: We show that a separating set for a representation can be obtained by adding, to a separating set for any subrepresentation, some explicitly defined invariant polynomials. Meanwhile, an explicit generating set for the invariant ring is known only in a handful of cases for these representations. © 2010 Elsevier Inc. All rights reserved.
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    Lexsegment and Gotzmann ideals associated with the diagonal action of Z/p
    (Springer Wien, 2011) Sezer, M.
    We consider a diagonal action of a cyclic group of prime order on a polynomial ring F[x1,...,xn]. We give a description of the actions for which the corresponding Hilbert ideal is Gotzmann when n = 2. Nevertheless, we show that there is a separating set of invariant monomials that generates a proper lexsegment ideal in the polynomial ring for all n. As well, we provide an algorithm to compute this set. © 2009 Springer-Verlag.
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    Separating invariants for the klein four group and cyclic groups
    (World Scientific Publishing, 2013-06-11) Kohls, M.; Sezer, M.
    We consider indecomposable representations of the Klein four group over a field of characteristic 2 and of a cyclic group of order pm with p, m coprime over a field of characteristic p. For each representation, we explicitly describe a separating set in the corresponding ring of invariants. Our construction is recursive and the separating sets we obtain consist of almost entirely orbit sums and products. © 2013 World Scientific Publishing Company