2017 Fiscal Year Final Research Report
Representation theory of Iwanaga-Gorenstein rings from the viewpont of tilting thoery
| Project/Area Number |
26800007
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | University of Yamanashi |
|---|
Principal Investigator |
YAMAURA Kota 山梨大学, 大学院総合研究部, 助教 (60633245)
|
|---|
| Project Period (FY) |
2014-04-01 – 2018-03-31
|
| Keywords | 岩永-Gorenstein環 / Cohen-Macaulay加群 / 三角圏 / 傾理論 |
|---|
| Outline of Final Research Achievements |
The purpose is to study the stable category of graded Cohen-Macaulay modules over graded Iwanaga-Gorenstein rings from the viewpoint of tilting theory. We have the following results.
1. For a one dimensional graded commutative Gorenstein ring A with some assumptions, the thick subcategory generated by the syzygies of graded simple modules in the stable category of graded Cohen-Macaulay A-modules has a silting object. Moreover, the thick subcategory has a tilting object if and only if either A is regular or the a-invariant of A is non-negative.
2. Let R be an algebra over a filed and C be a bimodule. Assume that the trivial extension A of R by C is Iwanaga-Gorenstein. Then the stable category of graded Cohen-Macaulay A-modules can be realized as an admissible subcategory of the bounded derived category of the category of finitely generated R-modules if the global dimension of R is finite.
|
| Free Research Field |
環の表現論
|
