On vertex leibniz algebras

Haisheng Li, Shaobin Tan, Qing Wang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this paper, we study a notion of what we call vertex Leibniz algebra. This notion naturally extends that of vertex algebra without vacuum, which was previously introduced by Huang and Lepowsky. We show that every vertex algebra without vacuum can be naturally extended to a vertex algebra. On the other hand, we show that a vertex Leibniz algebra can be embedded into a vertex algebra if and only if it admits a faithful module. To each vertex Leibniz algebra we associate a vertex algebra without vacuum which is universal to the forgetful functor. Furthermore, from any Leibniz algebra g we construct a vertex Leibniz algebra Vg and show that Vg can be embedded into a vertex algebra if and only if g is a Lie algebra.

Original languageAmerican English
Pages (from-to)2356-2370
Number of pages15
JournalJournal of Pure and Applied Algebra
Issue number12
StatePublished - Dec 2013

ASJC Scopus subject areas

  • Algebra and Number Theory


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