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<p>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&#xa0;series of vertex algebras and study the problem of embedding of a&#xa0;left-symmetric algebra into a&#xa0;vertex one preserving the normally ordered product.</p>

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THE GRÖBNER–SHIRSHOV BASES METHOD FOR VERTEX ALGEBRAS

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • R. A. Kozlov,
  • P. S. Kolesnikov

摘要

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.