TY - JOUR

T1 - On vertex leibniz algebras

AU - Li, Haisheng

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).

PY - 2013/12

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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U2 - https://doi.org/10.1016/j.jpaa.2013.04.001

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

M3 - Article

SN - 0022-4049

VL - 217

SP - 2356

EP - 2370

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 12

ER -