ℤ_𝑘-code vertex operator algebras

• Arakawa Tomoyuki

  Research Institute for Mathematical Sciences Kyoto University

• Yamada Hiromichi

  Department of Mathematics Hitotsubashi University

• Yamauchi Hiroshi

  Department of Mathematics Tokyo Woman's Christian University

Bibliographic Information

Other Title

• ℤ[k]-code vertex operator algebras
• $\mathbb{Z}_k$-code vertex operator algebras

Abstract

We introduce a simple, self-dual, rational, and 𝐶₂-cofinite vertex operator algebra of CFT-type associated with a ℤ_𝑘-code for 𝑘 ≥ 2. Our argument is based on the ℤ_𝑘-symmetry among the simple current modules for the parafermion vertex operator algebra 𝐾(𝔰𝔩₂, 𝑘). We show that it is naturally realized as the commutant of a certain subalgebra in a lattice vertex operator algebra. Furthermore, we construct all the irreducible modules inside a module for the lattice vertex operator algebra.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 73 (1), 185-209, 2021

  The Mathematical Society of Japan

Keywords

• vertex operator algebra
• parafermion algebra
• simple current
• code

Details

• CRID: 1391412881284773376
• NII Article ID: 130007973751
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/83278327
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• HANDLE: 2433/276267
• NDL BIB ID: 031231362
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I031231362
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed