2006 Fiscal Year Final Research Report Summary
Study of algebras relating to quadratic form by using representation theory and homological algebras
| Project/Area Number |
16540019
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | University of Yamanashi |
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Principal Investigator |
SATO Masahisa University of Yamanashi, Department of Research Interdisciplinary Graduate School of Medicine and Engineering, Professor, 大学院医学工学総合研究部, 教授 (30143952)
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| Co-Investigator(Kenkyū-buntansha) |
IWANAGA Yasuo Shinshu University, Faculty of Education, Professor, 教育学部, 教授 (80015825)
WAKAMATSU Takayoshi Saitama University, Faculty of Education, Professor, 教育学部, 教授 (00192435)
MIYAMOTO Izumi University of Yamanashi, Department of Research Interdisciplinary Graduate School of Medicine and Engineering, Professor, 大学院医学工学総合研究部, 教授 (60126654)
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| Project Period (FY) |
2004 – 2006
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| Keywords | algebra / quadratic form / representatuion theory / homology / cartan matrix / coxeter matrix / frobenius algebra / group |
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| Research Abstract |
In 2004, we attended two international conference, the fourth Japan-China-Korea Iternational symposium on ting theory held in Nanjing, China from July 24 to 26 and the 11th International conference on representation theory of algebras to introduce the recent results and observe the trend of study.
In 2005, we held the 38th ring and representation theory symposium in Aichi Institute of Technology and we invited professor Raphael Rouquier (University Denis Diderot-Paris 7) who study closely related us and asked him lectures about elementary theory for solving Broue conjecture. These achievement are published as the proceedings.
In 2006, we invited professor Izuru Mori to ask lectures about non-commutative algebraic geometry, which is expected an important field of non-commutative ring theory, including its history and the trend in abroad. Also we invited Kiyoshi Igusa (Brandise, U. S. A) and Professor Yao Mushung (Fudan, China).
Through these research with many mathematicians, we completed the research of some kind of quadratic forms and we get the characterization to be the quadratic form corresponding to a Cartan matrix of an algebra. Also we characterized these conditions by the periodicity of a Coxeter matrix of a Cartan matrix of an algebra. As the result, we showed that the characteristic root of a Coxeter matrix is algebraic integer and this plays important role in these study.
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Research Products
(22 results)
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[Journal Article] Oneway hereditary rings2005
Author(s)
Masahisa Sato
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Journal Title
The Proc. Of the 10th InternationalSympo-sium on Ring and Representation Theory, Fields Institute 45
Pages: 331-343
Description
「研究成果報告書概要(和文)」より
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[Journal Article] Oneway hereditary rings2005
Author(s)
Masahisa Sato
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Journal Title
The Proc. of the 10th InternationalSympo-sium on Ring and Representation Theory. Fields Institute 45
Pages: 331-343
Description
「研究成果報告書概要(欧文)」より
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[Book] 入門線型代数学2005
Author(s)
岩永 恭雄
Total Pages
264
Publisher
日本評論社
Description
「研究成果報告書概要(和文)」より
