2009 Fiscal Year Final Research Report
Generalized quantum groups, including super and elliptic ones, and Weyl groupoids
| Project/Area Number |
19540027
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
YAMANE Hiroyuki Osaka University, 大学院・情報科学研究科, 准教授 (10230517)
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| Co-Investigator(Kenkyū-buntansha) |
MIKI Kei 大阪大学, 大学院・情報科学研究科, 准教授 (40212229)
NAGATOMO Kiyokazu 大阪大学, 大学院・情報科学研究科, 准教授 (90172543)
OHYAMA Yousuke 大阪大学, 大学院・情報科学研究科, 准教授 (10221839)
KAWANAKA Noriaki 大阪大学, 大学院・情報科学研究科, 准教授 (10028219)
DATE Etsuro 大阪大学, 大学院・情報科学研究科, 教授 (00107062)
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| Project Period (FY) |
2007 – 2009
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| Keywords | ワイル亜群 / ニコルス代数 / 量子群 / スーパー代数 / ホップ代数 |
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| Research Abstract |
In 2006, Yamane, with Heckenberger, introduced axioms of Weyl groupoids and showed that Weyl groupoids satisfy a Matsumoto-type theorem. In 2008, using this result, they gave a factorization formula for the Shapovalov determinants of generalized quantum groups, including quantum superalgebras, by using the longest elements of the Weyl groupoids. This study is epoch-making since it was achieved by using intensively a special situation happened at roots of unity. Under some special conditions, simlar theorems were shown by several people, but their proofs were made by using the Shapovalov's original result for the simple Lie algebras.
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