On ℕ-graded vertex algebras associated with cyclic Leibniz algebras with small dimensions

2023/01/14 by C. Barnes, E. Martin, Barnes, C. +5
Mathematics · #17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2301.05902

openalex publication_date 2023/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main goals for this paper is i) to study of an algebraic structure of ℕ-graded vertex algebras V_B associated to vertex A-algebroids B when B are cyclic non-Lie left Leibniz algebras, and ii) to explore relations between the vertex algebras V_B and the rank one Heisenberg vertex operator algebra. To achieve these goals, we first classify vertex A-algebroids B associated to given cyclic non-Lie left Leibniz algebras B. Next, we use the constructed vertex A-algebroids B to create a family of indecomposable non-simple vertex algebras V_B. Finally, we use the algebraic structure of the unital commutative associative algebras A that we found to study relations between a certain type of the vertex algebras V_B and the vertex operator algebra associated to a rank one Heisenberg algebra.

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