On vertex leibniz algebras

Haisheng Li; Shaobin Tan; Qing Wang

doi:https://doi.org/10.1016/j.jpaa.2013.04.001

On vertex leibniz algebras

Haisheng Li, Shaobin Tan, Qing Wang

Rutgers Camden, Mathematics

Rutgers, The State University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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 language	American English
Pages (from-to)	2356-2370
Number of pages	15
Journal	Journal of Pure and Applied Algebra
Volume	217
Issue number	12
DOIs	https://doi.org/10.1016/j.jpaa.2013.04.001
State	Published - Dec 2013

ASJC Scopus subject areas

Algebra and Number Theory

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title = "On vertex leibniz algebras",

abstract = "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.",

author = "Haisheng Li and Shaobin Tan and Qing Wang",

note = "Funding Information: The first author was partially supported by NSA grant H98230-11-1-0161 and China NSF grant (No. 11128103). The second author was partially supported by China NSF grant (No. 10931006) and a grant from the Ph.D. Programs Foundation of Ministry of Education of China (No. 20100121110014). The third author was partially supported by China NSF grant (No. 11001229) and the Fundamental Research Funds for the Central University (No. 2012121004).",

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doi = "https://doi.org/10.1016/j.jpaa.2013.04.001",

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AU - Tan, Shaobin

AU - Wang, Qing

N1 - Funding Information: The first author was partially supported by NSA grant H98230-11-1-0161 and China NSF grant (No. 11128103). The second author was partially supported by China NSF grant (No. 10931006) and a grant from the Ph.D. Programs Foundation of Ministry of Education of China (No. 20100121110014). The third author was partially supported by China NSF grant (No. 11001229) and the Fundamental Research Funds for the Central University (No. 2012121004).

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Y1 - 2013/12

N2 - 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.

AB - 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.

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JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

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ER -

On vertex leibniz algebras

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