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On vertex Leibniz algebras.
- Source :
-
Journal of Pure & Applied Algebra . Dec2013, Vol. 217 Issue 12, p2356-2370. 15p. - Publication Year :
- 2013
-
Abstract
- 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 we construct a vertex Leibniz algebra and show that can be embedded into a vertex algebra if and only if is a Lie algebra. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00224049
- Volume :
- 217
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Journal of Pure & Applied Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 89108857
- Full Text :
- https://doi.org/10.1016/j.jpaa.2013.04.001