Orbifold constructions and holomorphic vertex operator algebras of central charge 24

2016 Fiscal Year Final Research Report

• Project/Area Number: 26800001
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Tohoku University
• Principal Investigator: Shimakura Hiroki 東北大学, 情報科学研究科, 准教授 (90399791)
• Research Collaborator: Ching Hung Lam 中央研究院, 数学研究所, 教授
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 代数学 / 頂点作用素代数 / 正則頂点作用素代数 / 軌道体構成法 / リー代数 / 内部自己同型

Outline of Final Research Achievements

The classification of holomorphic vertex operator algebras of central charge 24 is one of famous problems in vertex operator algebra theory. This problem has been studied based on the list of 71 possible weight one Lie algebra structures given by Schellekens in 1993.

At the beginning of this research project, there are the remaining 12 Lie algebras in the list such that the corresponding holomorphic vertex operator algebras have not been constructed yet. The main result is to establish the 6 cases of the remaining 12 cases by using orbifold constructions. Combining the results by us and other researchers, we have proved that for any Lie algebra in Schellekens' list, there exists a holomorphic vertex operator algebra of central charge 24 with it as the weight one Lie algebra.

Free Research Field

頂点作用素代数