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Research on clarifying algebraic structure of rings using each representation theory of algebras, group rings and Lie rings.

利用代数、群环和李环各自的表示论阐明环的代数结构的研究。

基本信息

批准号：
11640019
负责人：
SATO Masahisa
金额：
$ 2.05万
依托单位：
Yamanashi University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640019/
关键词：
Ring Representation Algebra Lie Algebra Noeterian Ring Group ring Association Scheme Noetherian ring association scheme

项目摘要

[1999]In Duality theory Sato studied the principle of Duality which exists in Commutative noetherian ring and analyzed it in the view point of general non-commutative ring theory. By using non-commutative ring theory method, he succeeded to find the essential principle that Duality exists. which was difficult to find in the case of commutative ring since several facts were mixed to be held one fact. Also he showed theses facts hold also in the case of non-commutative rings under some conditions.Miyamoto studied about Association scheme which is notified recently and he decided these which has elements up to 22.Iwanaga generalized Wakamatsu theorem, which is famous theorem in the field of the representation theory of algebras, with respect to Tilting algebra.Kurihara advised on researched through discussion about the above studies.[2000]Sato studied global dimension of typical case of quasi-hereditary rings which had been introduced from the representation theory of Lie algebras. For the ring you make the endomorphism ring of direct sum of all modules of the ring modulo the power of its Jacobson radical, then this ring becomes quasi-hereditary. He completely find the structure of minimal projective resolution of simple modules of this endomorphism ring and using this properties, he created the way of construction of resolution of these modules. Also he proved the global dimension does not exceed the number of simple modules.Miyamoto found the construction of groups which includes normalizer of permutation groups by using association scheme noticed as generalization of group rings.Iwanaga continued the study of the generalization of Wakamatsu theorem.Kurahara gave advises in the stand point of view of analysis through discussions.

[1999]在对偶理论中，佐藤研究了交换Notherian环中存在的对偶原理，并从一般非交换环论的角度对其进行了分析。他运用非对易环论的方法，成功地找到了对偶存在的基本原理。这在交换环的情况下很难找到，因为几个事实混合在一起被认为是一个事实。他还证明了这些事实在某些条件下也适用于非交换环。宫本研究了最近公布的结合方案，他确定了元素不超过22的结合方案。关于倾斜代数，Iwanaga推广了Wakamatsu定理，这是代数表示论领域中著名的定理。栗原建议通过对上述研究的讨论来研究。[2000]Sato研究了从李代数表示理论引入的拟遗传环的典型情况的整体维度。对于环，使环的所有模的直和的自同态环以其Jacobson根的幂为模，则这个环成为拟遗传的。他完全找到了这个自同态环的单模的极小射影分解的结构，并利用这一性质，建立了这些模的分解的构造方法。他还证明了整体维度不超过单模的个数。宫本利用作为群环推广的结合方案发现了包含置换群的正规化子的群的构造。岩原继续研究了Wakamatsu定理的推广。栗原通过讨论从分析的角度给出了建议。