On Indecomposable Non-Simple ℕ-graded Vertex Algebras

2019/07/26 by Phichet Jitjankarn, Jitjankarn, Phichet, Gaywalee Yamskulna +1
Mathematics · #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.1907.11627

openalex publication_date 2019/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study an impact of Leibniz algebras on the algebraic structure of ℕ-graded vertex algebras. We provide easy ways to characterize indecomposable non-simple ℕ-graded vertex algebras ⊕_n=0^∞V_(n) such that dim V₍₀₎≥ 2. Also, we examine the algebraic structure of ℕ-graded vertex algebras V=⊕_n=0^∞V_(n) such that dim~V₍₀₎≥ 2 and V₍₁₎ is a (semi)simple Leibniz algebra that has sl₂ as its Levi factor. We show that under suitable conditions this type of vertex algebra is indecomposable but not simple. Along the way we classify vertex algebroids associated with (semi)simple Leibniz algebras that have sl₂ as their Levi factor.

Citations

• Vertex Algebroids II

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