Hilbert理想的Gröbner基与二面体群$D_{2p}$ }的共不变量
Gröbner bases for the Hilbert ideal and coinvariants of the Dihedral group $D_{2p}$}
摘要：
考虑了特征为2的域上二面体群$D_{2p}$的有限维表示，其中$p$是奇素数，并研究了相应的Hilbert理想$I_H$ .证明了$I_H$有一个仅由不变量和单项式组成的泛Gr\”{o}bner基.我们在此基础上，并在一个最小生成集的$I_H$的元素的程度提供了尖锐的界限。我们还计算了协不变项的最高度。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
