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]在二元性理论中，佐藤研究了二元性原理，该原理在诺瑟式的戒指中存在，并在一般的非共同环理论的角度进行了分析。通过使用非交流性环理论方法，他成功地找到了二元性存在的基本原则。在交换戒指的情况下，很难找到这是一个事实，因为有几个事实被认为是一个事实。他还向某些条件下的非交通戒指表明，这方面的事实也存在。Miyamoto研究了有关联想方案的研究，该计划最近被通知，他决定具有22.iwanaga概括的Wakamatsu定理，这是著名的定理，该理论是在Algebra.kurra.kurra.kur的表现方面的研究。研究。[2000] Sato研究了从谎言代数的代表理论中引入的准栖息环典型情况的全球维度。对于戒指，您使环模块的所有模块的直接总和的内态环具有其雅各布森激进的力量，然后该戒指变成Quasi Herditary。他完全找到了该内态圆环简单模块的最小投影分辨率的结构，并使用了这些属性，创造了这些模块分辨率的构建方式。他还证明，全球维度不超过简单模块的数量。Miyamoto发现了组的构造，其中包括置换组的归一化器，使用关联方案注意，这是对组环的概括。