2016 Fiscal Year Final Research Report
Studies on conformal algebras and Lie algebras
| Project/Area Number |
26610007
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 共形代数 / 頂点作要素代数 / リー代数 / 圏同値 |
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| Outline of Final Research Achievements |
Conformal algebras have finitely many products which are parametrized by natural numbers. In this project we prove the equivalence of categories between the category of conformal algebras and the category of Lie algebra. Therefore, we can define the notion of conformal algebras by a single product called the Lie bracket. (The definition of conformal algebras are very complicated because of infinitely many products.) To prove the equivalence of categories we introduced the notion of quasi-primitive projection which are used to define a Lie bracket on the space of quasi-primitive elements. In pour proof of the equivalence of categories, we found many identities on polynomial functions in four indeterminate, which will be applied to other areas of mathematics.
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| Free Research Field |
頂点作要素代数
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