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      Degree of reductivity of a modular representation

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      Author(s)
      Kohls, M.
      Sezer, M.
      Date
      2017
      Source Title
      Communications in Contemporary Mathematics
      Print ISSN
      0219-1997
      Electronic ISSN
      1793-6683
      Publisher
      World Scientific Publishing
      Volume
      19
      Issue
      3
      Pages
      1650023-1 - 1650023-12
      Language
      English
      Type
      Article
      Item Usage Stats
      198
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      165
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      Abstract
      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.
      Keywords
      Degree bounds
      Invariant theory
      Klein four group
      Modular groups
      Reductive groups
      Separating invariants
      13A50
      Permalink
      http://hdl.handle.net/11693/37070
      Published Version (Please cite this version)
      http://dx.doi.org/10.1142/S0219199716500231
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      • Department of Mathematics 688
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