1998 Fiscal Year Final Research Report Summary
Study on elucidation of Algebratc Structure of rings applying Representation Theories of Finite dimerstcrra algebhas, Griupalgerhras and Lie Alberas
| Project/Area Number |
09640022
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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 | YAMANASHI UNIVERSITY |
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Principal Investigator |
SATO Masahisa YAMANASHI UNIVERSITY,Faculty of Engineering, Professor, 工学部, 教授 (30143952)
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| Co-Investigator(Kenkyū-buntansha) |
KANASAWA Shuya Kanazawa University, Faculty of Engineering, Professor, 工学部, 教授 (50185899)
HANAKI Akihide Shinshu University, Faculty of Science, Lefessor, 理学部, 講師 (50262647)
KOMIYA Kaname YAMANASHI UNIVERSITY,Faculty of Engineering, Professor, 教育人間科学部, 教授 (60020327)
MIYAMOTO Izumi YAMANASHI UNIVERSITY,Faculty of Engineering, Associated Professor, 工学部, 助教授 (60126654)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Ring / Algebtaic Styocture / Algebra / Group Ring / Representation Theory / Lie Algebra / Group / Derived Category |
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| Research Abstract |
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 Representation
Theory 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.
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