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Using SAGBI Bases to Compute Rings of Invariants

  • H. E. A. Eddy CampbellEmail author
  • David L. Wehlau
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Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 139)

Abstract

In (Shank, 1998), Shank constructed generating sets, in fact, SAGBI bases, for the rings \(\mathbb{F}[V_{4}]^{C_{p}}\) and \(\mathbb{F}[V_{5}]^{C_{p}}\) for all primes p≥5. Of course, for the primes p=2,3, the corresponding actions are actions of \(C_{p^{2}}\) or \(C_{p^{3}}\), not C p . The rings of invariants \(\mathbb{F}[V_{4}]^{C_{4}}\), \(\mathbb{F}[V_{4}]^{C_{9}}\), \(\mathbb{F}[V_{5}]^{C_{8}}\) and \(\mathbb{F}[V_{5}]^{C_{9}}\) are all easily computed by computer, for example, using MAGMA.

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References

  1. 98.
    R. James Shank, S.A.G.B.I. bases for rings of formal modular seminvariants, Comment. Math. Helv. 73 (1998), no. 4, 548–565. MR 2000a:13016 zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Sir Howard Douglas Hall, Dept. MathematicsUniversity of New BrunswickFrederictonCanada
  2. 2.Dept. Mathematics & Computer ScienceRoyal Military College of CanadaKingstonCanada

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