Groebner--Shirshov bases method for vertex algebras

2023/12/04 by R. A. Kozlov, Kozlov, R. A., P. S. Kolesnikov +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2312.01670

openalex publication_date 2023/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we show how to apply the Gröbner--Shirshov bases (GSB) method for modules over an associative algebra to the study of vertex algebras defined by generators and relations. We compute GSBs for a series of vertex algebras and study the problem of embedding of a left-symmetric algebra into a vertex one preserving the normally ordered product.

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