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
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
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© 2011 Springer-Verlag Berlin Heidelberg
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Campbell, H.E.A.E., Wehlau, D.L. (2011). Using SAGBI Bases to Compute Rings of Invariants. In: Modular Invariant Theory. Encyclopaedia of Mathematical Sciences, vol 139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17404-9_13
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DOI: https://doi.org/10.1007/978-3-642-17404-9_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17403-2
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