Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T13:29:47.757Z Has data issue: false hasContentIssue false
  • English
  • Français

Invariants of the dihedral group D2p in characteristic two

Published online by Cambridge University Press:  19 October 2011

MARTIN KOHLS  and
MÜFİT SEZER
MARTIN KOHLS
Affiliation:
Technische Universität München, Zentrum Mathematik-M11, Boltzmannstrasse 3, 85748 Garching, Germany. e-mail: [email protected]
MÜFİT SEZER
Affiliation:
Department of Mathematics, Bilkent University, Ankara 06800Turkey. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider finite dimensional representations of the dihedral group D2p over an algebraically closed field of characteristic two where p is an odd prime and study the degrees of generating and separating polynomials in the corresponding ring of invariants. We give an upper bound for the degrees of the polynomials in a minimal generating set that does not depend on p when the dimension of the representation is sufficiently large. We also show that p + 1 is the minimal number such that the invariants up to that degree always form a separating set. We also give an explicit description of a separating set.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 152 , Issue 1 , January 2012 , pp. 1 - 7
Copyright
Copyright © Cambridge Philosophical Society 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Derksen, H. and Kemper, G.Computational invariant theory. Invariant Theory and Algebraic Transformation Groups, I. (Springer-Verlag, 2002). Encyclopaedia of Mathematical Sciences, 130.CrossRefGoogle Scholar
[2]Derksen, H. and Kemper, G.Computing invariants of algebraic groups in arbitrary characteristic. Adv. Math. 217 (5) (2008), 2089–2129.CrossRefGoogle Scholar
[3]Draisma, J., Kemper, G. and Wehlau, D.Polarization of separating invariants. Canad. J. Math. 60 (3) (2008), 556–571.CrossRefGoogle Scholar
[4]Kemper, G.Separating invariants. J. Symbolic Comput. 44 (2009), 1212–1222.CrossRefGoogle Scholar
[5]Kohls, M. and Kraft, H.Degree bounds for separating invariants. Math. Res. Lett. 17 (6) (2010), 1171–1182.CrossRefGoogle Scholar
[6]Kohls, M. and Sezer, M. Separating invariants for the klein four group and the cyclic groups. arXiv:1007.5197, 2010.Google Scholar
[7]Schmid, B. J. Finite groups and invariant theory. In Topics in invariant theory (Paris, 1989/1990), volume 1478 of Lecture Notes in Math. pages 35–66 (Springer, 1991).Google Scholar
[8]Sezer, M.Constructing modular separating invariants. J. Algebra. 322 (11) (2009), 4099–4104.CrossRefGoogle Scholar
[9]Symonds, P. On the Castelnuovo-Mumford regularity of rings of polynomial invariants. Annals of Math., to appear. Preprint available from http://www.maths.manchester.ac.uk/~pas/preprints/, 2009.Google Scholar