2012 Fiscal Year Final Research Report
Development of a universal representation theory of generalized quantum enveloping algebras with structures of Coxeter groupoids
| Project/Area Number |
22540020
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Osaka University |
|---|
Principal Investigator |
YAMANE Hiroyuki 大阪大学, 大学院・人間科学研究科, 准教授 (10230517)
|
|---|
| Project Period (FY) |
2010 – 2012
|
| Keywords | ワイル亜群 / 一般化された量子群 / ニコルス代数 / 多変数アフィンリー代数 |
|---|
| Research Abstract |
Yamane with his coworkers made deeper studies of defining relations of multi-parameter quantum superalgebras and corresponding Nichols algebras. Yamane with his coworkers classified the finite dimensional irreducible highest weight modules of generalized quantum groups by using special reduced expressions of longest elements of Weyl groupoids. Yamane with his coworkers gave an explicit formulas of the universal R-matrices by using the quantum double construction. Yamane with his coworkers introduced a notion of the reflectable base, as a generalization of base, and classified them except for E-types.
|
