论文标题
二面体组的矢量不变的syzygies
Syzygies for the vector invariants of the dihedral group
论文作者
论文摘要
从定义$ 2 $维二维表示的$ m $ tuplacter上，发现二面群体代数的代数代数的生成器之间的关系的生成器的问题。结果表明，这种$ gl $ - 理想是由关系产生的，具体取决于不超过$ 3 $的向量变量。对于$ m = 2 $的情况，以及订单订单$ 8 $和任意$ m $的情况，发现了最小的$ gl $ - 理想生成系统。
The problem of finding generators of the $GL$-ideal of the relations between the generators of the algebra of invariants of the dihedral group acting on $m$-tuples of vectors from its defining $2$-dimensional representation is studied. It is shown that this $GL$-ideal is generated by relations depending on no more than $3$ vector variables. A minimal $GL$-ideal generating system is found for the case when $m=2$, and for the case of the dihedral group of order $8$ and arbitrary $m$.
