New methods of study in noncommutative algebraic geometry using representation theory of algebras
| Project/Area Number |
25400037
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Shizuoka University |
|---|
Principal Investigator |
MORI IZURU 静岡大学, 理学部, 教授 (50436903)
|
|---|
| Project Period (FY) |
2013-04-01 – 2016-03-31
|
| Project Status |
Completed (Fiscal Year 2015)
|
| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
|---|
| Keywords | 非可換代数幾何学 / 多元環の表現論 / AS-regular代数 / 量子射影空間 / 非可換環論 / 代数幾何学 / ＡＳ正則代数 / AS-regular algebra / Fano algebra / 非可換次数付孤立特異点 |
|---|
| Outline of Final Research Achievements |
Noncommutative algebraic geometry is a recently established research field, which studies algebras using tools from algebraic geometry. AS-regular algebras and quantum projective spaces are main objects of study in noncommutative algebraic geometry. The major achievement of this research project is that, by using tools not only from algebraic geometry, but also from representation theory of algebras, such as theory of n-representation infinite algebras, theory of superpotentials and theory of isolated singularities, we studied and classified AS-regular algebras and quantum projective spaces.
|
Report
(4 results)
Research Products
(17 results)
