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

1997年，我们举办了第30届环理论与表征理论研讨会（10月20日至23日，长野，新州大学），我们邀请了加拿大卡尔顿大学的V.DIab教授，他一直在研究与我们的研究密切相关的问题。研究成果发表在第30届环理论与表征理论学术研讨会论文集上。在环理论的基础上，从李环和关联方案的角度对群环进行了研究。此外，我们还利用同调方法研究了与表示理论密切相关的自反模。我们参加了很多学术会议来展示我们的成果，通过参加相关会议我们获得了很多信息。1998年，我们参加了在德国比勒菲尔德举行的代数表示理论国际会议，并展示了我们的成果。此外，他还访问了捷克的查尔斯大学，会见了V.DIab教授（他也是加拿大卡尔顿大学的教授，我们在1997年通过该基金邀请了他）。他回顾了我们的研究结果。我们邀请了筑波大学的星野教授来获取关于派生范畴的信息，这对现在研究环理论似乎很重要。与1997年一样，我们继续积极参加许多会议，以促进我们的学习。通过使用范畴方法，我们可以在表示理论中进行比森田等价或环同构更广泛的分类，并找到了更精确地描述环间内部关系的方法。

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.