2011 Fiscal Year Final Research Report
Capelli type identities and enveloping algebras of Lie algebras
| Project/Area Number |
20740020
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Kagoshima University |
|---|
Principal Investigator |
ITOH Minoru 鹿児島大学, 大学院・理工学研究科, 准教授 (60381141)
|
|---|
| Project Period (FY) |
2008 – 2011
|
| Keywords | テンソル代数 / dual pair / 外積代数 / 不変式論の第一・第二基本定理 / Cayley-Hamiltonの定理 / 普遍包絡環の中心元 / 量子群 |
|---|
| Research Abstract |
The first result is the notion of derivations on tensor algebras and its applications to the invariant theory of noncommutative algebras(e. g. tensor algebras or universal enveloping algebras of Lie algebras). I also obtained a q-analogue of these results. The second result is some series of first and second fundamental theorems of invariant theory for polynomial algebras and exterior algebras. We have Cayley-Hamilton type theorems behind these second fundamental theorems. In addition, these second fundamental theorems for exterior algebras are closely related to the theory of polynomial identities.
|
