Representations of a fixed-point subalgebra of a class of lattice vertex operator algebras by an automorphism of order three

This is a summary of our recent work. We study a fixed-point subalgebra of a certain class of lattice vertex operator algebras by an automorphism of order 3, which is a lift of a fixed-point-free isometry of the underlying lattice. The classification of the irreducible modules, together with the rat...

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Bibliographic Details
Published inEuropean journal of combinatorics Vol. 30; no. 3; pp. 725 - 735
Main Authors Tanabe, Kenichiro, Yamada, Hiromichi
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.04.2009
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Summary:This is a summary of our recent work. We study a fixed-point subalgebra of a certain class of lattice vertex operator algebras by an automorphism of order 3, which is a lift of a fixed-point-free isometry of the underlying lattice. The classification of the irreducible modules, together with the rationality and the C 2 -cofiniteness of the subalgebra are established. Our result contains the case of the vertex operator algebra associated with the Leech lattice.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2008.07.002