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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/28545
Title: | 有限正交群的不變多項式 Polynomial Invariants of Orthogonal Groups of Finite Characteristics |
Authors: | Hsiang-Chun Hsu 徐祥峻 |
Advisor: | 朱樺 |
Keyword: | 模正交群,不變多項式,完全交, modular orthogonal group,polynomial invariants,complete intersection, |
Publication Year : | 2007 |
Degree: | 碩士 |
Abstract: | 令 $Bbb F_q$ 是有 $q$ 個元素的 Galois 體, $Q_n$ 是 $Bbb F_q^n$ 上的非退化二次型且 $O_n(Bbb F_q)$ 是由 $Q_n$
定義的正交群。 令 $O_n(Bbb F_q)$ 線性地作用於多項式環 $Bbb F_q[x_1,x_2,dots,x_n]$ 上。 在本論文中, 我們將確切地 找出 $O_n(Bbb F_q)$ 的不變子環的生成元及其關係, 並且證明此不變子環是唯一分解環及完全交。 Let $Bbb F_q$ be the Galois field with $q$ elements, $Q_n$ a non-degenerated quadratic form on $Bbb F_q^n$, and $O_n(Bbb F_q)$ the orthogonal group defined by $Q_n$. Let $O_n(Bbb F_q)$ act linearly on the polynomial ring $Bbb F_q[x_1,x_2,dots,x_n]$. In this paper, we will find explicit generators and relations for the ring of invariants of $O_n(Bbb F_q)$, and prove that it is a UFD and a complete intersection. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/28545 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 數學系 |
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