2006 Fiscal Year Final Research Report Summary
Elliptic Lie (super)algebras, affine Lie superalgebras and their quauntum groupsand their representation theories
| Project/Area Number |
16540026
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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, Graduate School of Information Science and Technology, Associate Professor, 大学院情報科学研究科, 助教授 (10230517)
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| Co-Investigator(Kenkyū-buntansha) |
HIBI Takayuki Osaka University, Graduate School of Information Science and Technology, Associate Professor, 大学院情報科学研究科, 教授 (80181113)
KAWANAKA Noriaki Osaka University, Graduate.School of Information Science and Technology, Associate Professor, 大学院情報科学研究科, 教授 (10028219)
DATE Etsurou Osaka University, Graduate School of Information Science and Technology, Associate Professor, 大学院情報科学研究科, 教授 (00107062)
NAGATOMO Kiyokazu Osaka University, Graduate School of Information Science and Technology, Associate Professor, 大学院情報科学研究科, 助教授 (90172543)
MIKI Kei Osaka University, Graduate School of Information Science and Technology, Associate Professor, 大学院情報科学研究科, 助教授 (40212229)
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| Project Period (FY) |
2004 – 2006
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| Keywords | Elliptic Lie algebras / Elliptic Lie superalgebras / Elliptic quantum groups / Super quantum groups / Z / 3Z quantum groups / Coxeter groups / Coxeter groupoids / Word problem of semigroups |
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| Research Abstract |
Coxeter semigroups (groupoids) and an associated Matsumoto-type theorem were studied. Yamane, in a joint work with Heckenberger, intruduced a notion of the Coxeter semigroups, being inspired by research of Lie superalgebras and Nicols algebras. He also showed a Matsumot-type theorem, that is, any two elements of the Coxeter semigroups having the same length are transformed from one to the other by the Coxeter (braid) relations only. Miki studied the type A quantum toroidal algebras and Macdonald's defference operators.
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