Gröbner bases for the Hilbert ideal and coinvariants of the Dihedral group $D_{2p}$}

Details Gröbner bases for the Hilbert ideal and coinvariants of the Dihedral group $D_{2p}$} Gröbner bases for the Hilbert ideal and coinvariants of the Dihedral group $D_{2p}$}

2011-09-28

arxiv.org/abs/1109.6180v1

Mathematics

Commutative Algebra

8 pages

Scientific paper

We consider a finite dimensional representation of the dihedral group $D_{2p}$ over a field of characteristic two where $p$ is an odd prime and study the corresponding Hilbert ideal $I_H$. We show that $I_H$ has a universal Gr\" {o}bner basis consisting of invariants and monomials only. We provide sharp bounds for the degree of an element in this basis and in a minimal generating set for $I_H$. We also compute the top degree of coinvariants.

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