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arXiv 1507.081422015-07math.RTmath.QA

全纯顶点算子代数的构造与分类

Construction and Classification of Holomorphic Vertex Operator Algebras

Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）；Technische Universität Darmstadt（达姆施塔特工业大学）

Jethro van Ekeren, Sven Möller, Nils R. Scheithauer

备注：: 37 pages, LaTeX; minor changes: numbering changed in Section 5, added results in Section 7, expanded Section 8; to appear in J. Reine Angew. Math. (Crelles Journal)
发表信息：: J. Reine Angew. Math. (Crelle's Journal), 759:61-99, 2020
DOI：: 10.1515/crelle-2017-0046

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AI总结：

该研究发展了作用于全纯顶点算子代数的有限循环群轨形理论，证明中心荷24的亚纯共形场论V₁结构的Schellekens分类为顶点算子代数定理，并据此构造出若干新的中心荷24的全纯顶点算子代数。

摘要：

我们发展了作用于全纯顶点算子代数的有限循环群的轨形理论。随后证明，中心荷为24的亚纯共形场论的V₁结构的Schellekens分类是顶点算子代数领域的一条定理。最后利用这些结果，以格轨形的形式构造了若干新的中心荷为24的全纯顶点算子代数。

英文摘要：

We develop an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras. Then we show that Schellekens' classification of $V_1$-structures of meromorphic conformal field theories of central charge 24 is a theorem on vertex operator algebras. Finally we use these results to construct some new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds.

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