2013 Fiscal Year Final Research Report
A study of infinite dimensional algebraic groups and Lie algebras, and an application to words and sequences
| Project/Area Number |
23540006
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | University of Tsukuba |
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Principal Investigator |
MORITA Jun 筑波大学, 数理物質系, 教授 (20166416)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 代数群 / リー代数 / 単純群 / 局所アフィン・リー代数 / 準周期構造 / オートマトン |
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| Research Abstract |
In the case when rank 2 hyperbolic Kac-Moody groups have trivial commutation relations, we obtained that the groups over certain infinite fields are simple modulo their centers. That is, if we suppose that a rank 2 hyperbolic Cartan matrix has no -1 entry, and if we choose the algebraic closure of a finite field, then we can obtain the simplicity of our group. We also classified the locally affine Lie algebras. Furthermore, we showed that there is an interesting correspondence between fundamental automata and hierarchy of numbers.
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