Pseudo-derivations and modular invariant theory
Pseudo-derivations and modular invariant theory
复制标题
伪导数和模不变理论
DOI：
10.1007/s00031-017-9461-6
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Ryuji Tanimoto
中科院分区：
文献类型：
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作者：
Shigeru Kuroda;Ryuji Tanimoto;Ryuji Tanimoto
让k成为一个具有积极特征的领域。引入ak-代数A的伪导子的概念，并给出了A的所有伪导子的集合与A的所有p-幂单自同构的集合之间的一一对应.本文将三元多项式环k [x，y，z]的p-幂单三角自同构分类到k [x，y，z]的自同构的共轭。本文证明了：若准循环群<$/p <$在多项式环k [x，y，z]上三角作用，则模不变环k [x，y，z]<$/p <$是超曲面环.
Letkbe a field of positive characteristicp. We introduce the notion of a pseudo-derivation of ak-algebraA, and give a one-to-one correspondence between the set of all pseudo-derivations ofAand the set of allp-unipotent automorphisms ofA. We classifyp-unipotent triangular automorphisms of a polynomial ringk[x,y, z] in three variables overkup to conjugation of automorphisms ofk[x,y, z]. We prove that if ap-cyclic groupℤ/pℤacts triangularly on the polynomial ringk[x,y,z], the modular invariant ringk[x,y,z]ℤ/pℤis a hypersurface ring.