Study on elucidation of Algebratc Structure of rings applying Representation Theories of Finite dimerstcrra algebhas, Griupalgerhras and Lie Alberas

应用有限二聚代数、Griupalgerhras和Lie Alberas表示论阐明环代数结构的研究

• 批准号: 09640022
• 负责人: SATO Masahisa
• 金额: $ 1.79万
• 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: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640022/
• 关键词: Ring; Algebtaic Styocture; Algebra; Group Ring; Representation Theory; Lie Algebra; Group; Derived Category; 代数:構造

We held the 30th Ring Theory and Representation Theory Symposium in 1997(October 20-23, Nagano, Shinshu-University) and we invited Professor V.DIab from Carleton University in Canada, who has been studying what was closely related to our study.These achievement was published to Proceeding of the 30th Ring Theory and Representation Theory Symposium.Group rings was studied in the stand point of view of Lie ring and association scheme in addition to the ring theoretical point of view.Also we studied about reflexive modules by using homological method, which is closely related to the representation theory.We attended to many academic meetings to present our results and we get much information by attending related meetings.In 1998, we attended to the International Conference of the RepresentationTheory of Algebra held at Bielefeld in Germany to present our results.In addition, e visited Charles University in Plague in Czech to meet to Professor V.DIab (who is also Professor of Carleton University in Canada and we invited him in 1997 by this fund). He reviewed our results.We invited Professor Hoshino from Tsukuba University to get information about Derived Category which seems to be important to study ring theory from now.Same as 1997, we continued to attend many meetings aggressively to promote our study.By using categorical method, in representation theory we can classify more wideIy than Morita equivalence or ring isomorphism and we found the way to develop our method for describing more precisely the internal relations between rings.

我们在1997年举行了第30圈理论和代表理论研讨会（10月20日至23日，Nagano，sinshu-University），我们邀请了加拿大卡尔顿大学的V.-Dib教授，他一直在研究与我们的研究密切相关的事情。我们还通过使用同源方法研究了反射模块，这与代表理论密切相关。我们参加了许多学术会议，以呈现我们的成绩，并通过参加相关会议来获得很多信息。 V.Diab教授（他也是加拿大卡尔顿大学的教授，我们于1997年由该基金邀请他）。他审查了我们的结果。我们邀请了来自杜库巴大学的Hoshino教授获取有关派生类别的信息，这对于从现在开始研究戒指理论似乎很重要。Same作为1997年，我们继续积极参加许多会议以促进我们的学习。使用分类方法，在代表性中，我们可以对Morita Equivalence或Ring Indressement seprients Indersiss Indression and Indersiss Indersiss进行分类，以使我们的内部关系更加范围。

项目成果

宮本泉: "One-relator Products of Two Groups of order three with short Relate" Kyushu J.Math.52. 81-97 (1998)

Izumi Miyamoto：“具有短相关的三阶两组的单相关乘积”Kyushu J.Math.52 (1998)。

金川秀也: "Error estimetion for discretized Euler-Maruyama scheme for SDE" Proc.of the Workshop on Turbelent Dibf and the relatel Publems in Stochastic Numeries,Inst.Ststist.Matbs Tokyo. 1. 139-157 (1996)

Hideya Kanakawa：“SDE 的离散 Euler-Maruyama 方案的误差估计”Proc.of the Workshop on Turbelent Dibf and the related Publems in Stochastic Numeries，Inst.Ststist.Matbs Tokyo 1. 139-157 (1996)。

花木章秀: "Self dual groups of order p^5 (p an odel prime)" Osaka Journal of Mathematices. 34. 357-361 (1997)

Akihide Hanaki：“p^5 阶自对偶群（p 一个奥德尔素数）” 大阪数学杂志 34. 357-361 (1997)。

宮本 泉: "One-relator Products of Two Groups of order three with short Relator" Kyushu J.Math.52. 81-97 (1998)

Izumi Miyamoto：“具有短关系器的两组三阶一关系器积”九州 J.Math.52（1998）。

Masahisa Sato: "Congectures of Ring Theory arrising from Recent Result" Yamanashi University Report. 48. 25-27 (1997)

佐藤正久：“从最近的结果中得出的环理论的构想”山梨大学报告。