Research on algebraic properties of categories of modules and structures of Frobenius algebras

Frobenius代数模范畴和结构的代数性质研究

• 批准号: 19540014
• 负责人: YAMAGATA Kunio
• 金额: $ 2.66万
• 依托单位: Tokyo University of Agriculture and Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2008
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540014/
• 关键词: 環; 多元環; 加群; 表現; 圏; クイバー; 有限次元多元環; Frobenius多元環; 入射加群; 準同型環; 部分圏

多元環の構造とその上の加群の成す圏について研究を行い、加群の直既約部分加群の直和分解と加群の準同型環との関係や、Cohen-Macaulay加群の分類、有限次元群多元環のFrobenius多元環としてのカルタン行列の持つ性質、加群圏の被覆理論の拡張と応用などについて多くの成果を上げた。これらの諸成果は本研究組織の各研究者によって国内外の国際研究集会やシンポジウムなどで発表され専門雑誌に掲載された

The structure of multi-dimensional rings and the relationship between the direct sum decomposition of the direct reduced partial addition groups and the quasi-isotypic rings of the addition groups are studied. The classification of Cohen-Macaulay addition groups. The properties of Frobenius multi-dimensional rings of finite dimensional groups. The results of the theory of covering of the addition groups are presented. The results of this study were published by the researchers of this research organization at international research conferences at home and abroad.

项目成果

Cartan matrices of symmetric algebras having generalized standard stable tubes

具有广义标准稳定管的对称代数嘉当矩阵

• 发表时间: 2008
• 期刊: Osaka Journal of Mathematics vol.45
• 作者: J. Bialkowski;A. Skowronski;and K. Yamagata
• 通讯作者: and K. Yamagata

Eigenvalues of Cartan matrices of principal 2-blocks with abelian defect groups

具有阿贝尔缺陷群的主2-块嘉当矩阵的特征值

• 发表时间: 2008
• 期刊: J. Algebra vol.319
• 作者: N. Kunugi;and T. Wada
• 通讯作者: and T. Wada

Universal lifts of chain complexes over non-commutativeparameter algebras

非交换参数代数上链复形的通用升力

• 发表时间: 2008
• 期刊: Journal of Mathematics of Kyoto University 48
• 作者: N. Kunugi;and T. Wada;H. Asashiba;Andrzej Skowronski;Osamu Iyama;Yuji Yoshino
• 通讯作者: Yuji Yoshino

Selfinjective algebras of quasitilted type

准倾斜型自射代数

• 发表时间: 2008
• 期刊: Trends in representation theory of algebras and related topics
• 作者: A. Skowronski;and K. Yamagata
• 通讯作者: and K. Yamagata

Domestic canonical algebras and simple Lie algebras

国内规范代数和简单李代数

• 发表时间: 2008
• 期刊: Math.Z vol.259
• 作者: N. Kunugi;and T. Wada;H. Asashiba
• 通讯作者: H. Asashiba