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- Material Type
- 規格・テクニカルリポート類
- Title
- Author/Editor
- 伊藤, 稔
- Publication, Distribution, etc.
- Alternative Title
- Capelli type identities and enveloping algebras of Lie algebras
- Target Audience
- 一般
- Note (General)
- 出版タイプ： VoR2008-2011年度科学研究費助成事業(科学研究費補助金(若手研究(B)))研究成果報告書 課題番号：20740020 研究代表者：伊藤稔 (鹿児島大学大学院理工学研究科(理学系)准教授)第一の成果は, テンソル代数における微分概念を導入して, それをテンソル代数やリー環の普遍包絡環などの非可換代数における不変式論に応用したことである. さらにこの結果のq類似も得た. 第二の成果は, 多項式環と外積代数における不変式論の第一・第二基本定理の多くの系列の発見である. この第二基本定理の背後にはCayley-Hamilton型の定理があり, 外積代数の結果についてはPolynomial Identityの理論との結びつきも得た.The first result is the notion of derivations on tensor algebras and its applications to the invariant theory of noncommutative algebras (e.g. tensor algebras or universal enveloping algebras of Lie algebras). I also obtained a q-analogue of these results. The second result is some series of first and second fundamental theorems of invariant theory for polynomial algebras and exterior algebras. We have Cayley-Hamilton type theorems behind these second fundamental theorems. In addition, these second fundamental theorems for exterior algebras are closely related to the theory of polynomial identities.
- Format (IMT)
- application/pdf
- Source
- 20740020seika.pdf （fulltext）