| Project/Area Number |
14340007
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Shinshu University |
|---|
Principal Investigator |
NISHIDA Kenji Shinshu University, Faculty of Science, Professor, 理学部, 教授 (70125392)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
IWANAGA Yasuo Shinshu University, Faculty of Education, Professor, 教育学部, 教授 (80015825)
NINOMIYA Yasushi Shinshu University, Faculty of Science, Professor, 理学部, 教授 (40092887)
YAMAGATA Kunio Tokyo University of Agriculture and Technology, Faculty of Technology, Professor, 工学部, 教授 (60015849)
KOSHITANI Shigeo Chiba University, Faculty of Science, Professor, 理学部, 教授 (30125926)
HIRANO Yasuyuki Okayama University, Faculty of Science, Assistant Professor, 理学部, 助教授 (90144732)
藤田 尚昌 筑波大学, 数学系, 講師 (60143161)
|
|---|
| Project Period (FY) |
2002 – 2004
|
| Project Status |
Completed (Fiscal Year 2004)
|
| Budget Amount *help |
¥10,200,000 (Direct Cost: ¥10,200,000)
Fiscal Year 2004: ¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2003: ¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2002: ¥3,600,000 (Direct Cost: ¥3,600,000)
|
|---|
| Keywords | Gorenstein ring / linkage / Cohen-Macaulay module / Hecke algebra / Broue conjecture / Aritinian ring / tiled order / ガロア被覆 / ヘッケ環 / ネータ多元環 / ゴレンシュテイン次元 / クイバー / フロべニウス多元環 / 整環 / アルテイン多元環 / ベーア環 / 群多元環 / フロベニウス多元環 / アルティン多元環 |
|---|
| Research Abstract |
We generalize Auslander formula. Then we get a short exact sequence which gives a relation between linkage and duality. Applying this result to commutative Gorenstein local rings, we get the fact that a finitely generated module is maximal Cohen-Macaulay if and only if its linkage module is maximal Cohen-Macaular and it is horizontally linkaged.
We determine a p-group G satisfying Hasse principle. We study commutativity of Hecke algebra through its character. Then we determine the condition of the prime number p and of the structure of G so as the Hecke algebra to be commutative under the assumption that G is p-nilpotent and the order of H, a Sylow p-subgroup of G, is equal to p.
We solved partly the Broue conjecture, one of the most important problem of modular representation theory of finite groups. We proved Broue conjecture is true for the principle block when the order of the Sylow p-subgroup of a finite group is equal to 9. Further, we proved the Broue conjecture is true for a non-principle block having a defect group of an order 9, whenever the groups under consideration are some important sporadic finite simple groups.
We proved that every residue ring is not right Artinian if and only if every right R-module which has a composition series is cyclic. Then we showed that this property is preserved under a finite normalizing extension and Morita equivalence.
We study a full matrix algebra defined by a structure system and then a Frobenius full matrix algebra. This algebra is related to a Gorenstein tiled order.
|
