Study on Representation Theory

表征论研究

• 批准号: 63540039
• 负责人: KAWADA Yutaka
• 金额: $ 0.9万
• 依托单位: Kyoto Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1988
• 资助国家: 日本
• 起止时间: 1988 至 1989
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63540039/
• 关键词: mod_PA; Transpose; Finite representation type; m.s.s. (minimal spanning system); Fit matrix theory; fit matrix theory; modpA; 表現順馳型(tamc type); 極小生成系(m・s・s); mod_pA; A-R系列; ディンキン図形; 表現有限型; A-R-グラフ

The purpose of this research project is to study representation theory of Artinian rings (of finite representation type). For the representation of finite-dimensional algebras over a field there were discovered various methods. But these methods can not always apply to our case. So we had to seek a new method.We first investigate Auslander-Bridger's duality over a semiperfect ring A. To clarify the content of the duality we shall adopt a restricted matrix theory over A, which is called the fit matrix theory over A, and define a relation matrix R for a module M, non-projective and finitely presented. Then, by means of R, we can succeed in a characterization for M to be in mod_p A, in a framework of the fit matrix theory over A.Grant-in-Aid for Scientific Research (C) has enabled us to cover the travel expenses to participate in the symposia, seminars, formal or informal meetings in related topics and fields.

本研究的目的是研究Artin环(有限表示型)的表示理论。对于域上有限维代数的表示，人们发现了各种方法。但这些方法并不总是适用于我们的情况。我们首先研究了半完美环A上的Auslander-Bridger对偶。为了阐明对偶的内容，我们将采用A上的一个限制矩阵理论，称为A上的Fit矩阵理论，并定义一个非投射的有限表示的模M的关系矩阵R。然后，借助于R，我们可以在A上的Fit矩阵理论的框架内，成功地刻画M在mod_p_A中。科学研究补助金(C)使我们能够支付参加相关主题和领域的座谈会、研讨会、正式或非正式会议的旅费。

项目成果

Hiroyuki Okura: Forum Mathematicum. 1. (1989)

大仓宏之：数学论坛。

Fumio Maitani: "Covering Properties of Extremal Vertical Slit Mappings" The Kodai Mathematical Journal, 11, 361-371, 1988.

Fumio Maitani：“极值垂直狭缝映射的覆盖特性”The Kodai Mathematical Journal，11, 361-371，1988。

Fumio Maitani: "Covering Properties of Extremal Vertical Slit Mappings" The Kodai Mathematical Journal. 11. 361-371 (1988)

Fumio Maitani：“极值垂直狭缝映射的覆盖特性”Kodai 数学杂志。

Fumio Maitani: "Variational formulas under quasiconformal deformation" Pitman Research Notes in Mathematics Series. 212. 105-122 (1989)

Fumio Maitani：“拟共形变形下的变分公式”皮特曼数学系列研究笔记。

Hiroyuki Okura: "Recurrence criteria for skew products of symmetric Markov processes" Forum Mathematicum. 1. 331-357 (1989)

Hiroyuki Okura：“对称马尔可夫过程的斜积的重现标准”数学论坛。