Classification of the vertex operator algebras VL+ of class S4

Tomonori Hashikawa; Hiroki Shimakura

doi:10.1016/j.jalgebra.2016.01.035

Classification of the vertex operator algebras V_L⁺ of class S⁴

Tomonori Hashikawa, Hiroki Shimakura

INF - Computer and Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we prove that an even rootless lattice L is isomorphic to 2A₁, √2D₄, √2E₈, or BW₁₆ if the lattice type vertex operator algebra V_L⁺ is of class S⁴. In addition, we prove that the vertex operator algebra V_√2D4⁺ is of class S⁵, and the vertex operator algebras V_2A1⁺, V_√2E8⁺, and V_BW16⁺ are of class S⁷.

Original language	English
Pages (from-to)	151-181
Number of pages	31
Journal	Journal of Algebra
Volume	456
DOIs	https://doi.org/10.1016/j.jalgebra.2016.01.035
Publication status	Published - 2016 Jun 15

Keywords

Binary codes
Lattices
Vertex operator algebras

ASJC Scopus subject areas

Algebra and Number Theory

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title = "Classification of the vertex operator algebras VL+ of class S4",

abstract = "In this paper, we prove that an even rootless lattice L is isomorphic to 2A1, √2D4, √2E8, or BW16 if the lattice type vertex operator algebra VL+ is of class S4. In addition, we prove that the vertex operator algebra V√2D4+ is of class S5, and the vertex operator algebras V2A1+, V√2E8+, and VBW16+ are of class S7.",

keywords = "Binary codes, Lattices, Vertex operator algebras",

author = "Tomonori Hashikawa and Hiroki Shimakura",

note = "Funding Information: The authors wish to thank Prof. Ching Hung Lam for his useful comments and various advices on the subject. They also wish to thank Dr. Motohiro Ishii for several helpful comments. The second author was partially supported by JSPS KAKENHI Grant Numbers 23540013 and 26800001 , and by Grant for Basic Science Research Projects from The Sumitomo Foundation , Grant Number 130032 . ",

year = "2016",

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doi = "10.1016/j.jalgebra.2016.01.035",

language = "English",

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journal = "Journal of Algebra",

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T1 - Classification of the vertex operator algebras VL+ of class S4

AU - Hashikawa, Tomonori

AU - Shimakura, Hiroki

N1 - Funding Information: The authors wish to thank Prof. Ching Hung Lam for his useful comments and various advices on the subject. They also wish to thank Dr. Motohiro Ishii for several helpful comments. The second author was partially supported by JSPS KAKENHI Grant Numbers 23540013 and 26800001 , and by Grant for Basic Science Research Projects from The Sumitomo Foundation , Grant Number 130032 .

PY - 2016/6/15

Y1 - 2016/6/15

N2 - In this paper, we prove that an even rootless lattice L is isomorphic to 2A1, √2D4, √2E8, or BW16 if the lattice type vertex operator algebra VL+ is of class S4. In addition, we prove that the vertex operator algebra V√2D4+ is of class S5, and the vertex operator algebras V2A1+, V√2E8+, and VBW16+ are of class S7.

AB - In this paper, we prove that an even rootless lattice L is isomorphic to 2A1, √2D4, √2E8, or BW16 if the lattice type vertex operator algebra VL+ is of class S4. In addition, we prove that the vertex operator algebra V√2D4+ is of class S5, and the vertex operator algebras V2A1+, V√2E8+, and VBW16+ are of class S7.

KW - Binary codes

KW - Lattices

KW - Vertex operator algebras

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