Geodesic
The Gr\"obner--Shirshov bases method for vertex algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 25 (2024) no. 1, pp. 103-122

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In the paper, we show how to apply the Gröbner–Shirshov bases method for modules over an associative algebra to the study of vertex algebras defined by generators and relations. We compute Gröbner–Shirshov bases 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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     title = {The {Gr\"obner--Shirshov} bases method for vertex algebras},
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R. A. Kozlov; P. S. Kolesnikov. The Gr\"obner--Shirshov bases method for vertex algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 25 (2024) no. 1, pp. 103-122. http://geodesic.mathdoc.fr/item/FPM_2024_25_1_a6/