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This work explores the structural properties of a specific class of vertex operator algebras and their uniqueness.

February 2, 2026Journal of Algebra and Its Applications0 citations

A class of vertex operator algebras with building blocks L ( c m ,0)

RFRunkang FengShanghai Jiao Tong University CJCuipo Jiang

Key Points

This work explores the structural properties of a specific class of vertex operator algebras and their uniqueness.
Defined a moonshine-type vertex operator algebra generated by Virasoro vectors of central charge
Proven uniqueness of the algebra given the simplicity of the Griess algebra
Proved simplicity of specific parafermion subalgebras
Showed that the vertex operator algebra is uniquely determined by its Griess algebra when simple
Demonstrated that the parafermion subalgebra is simple and isomorphic to a specific root system

Abstract

Let Formula: see text be a moonshine-type vertex operator algebra generated by Virasoro vectors Formula: see text of central charge Formula: see text, where Formula: see text, such that the Virasoro vertex operator algebra generated by Formula: see text is simple, Formula: see text, and Formula: see text for distinct Formula: see text. We prove that if Formula: see text is simple, then Formula: see text is uniquely determined by its Griess algebra Formula: see text. If Formula: see text, we further prove that Formula: see text is simple. As a result, we deduce that the subalgebra Formula: see text of the parafermion vertex algebra Formula: see text generated by Formula: see text, for Formula: see text, is simple and isomorphic to Formula: see text, where Formula: see text is the root system of Formula: see text.

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