Affiliation:
1. Departamento de Matemáticas, Cinvestav, Ciudad de México, México
Abstract
Abstract
In this note, we interpret Leibniz algebras as differential graded (DG) Lie algebras. Namely, we consider two fully faithful functors from the category of Leibniz algebras to that of DG Lie algebras and show that they naturally give rise to the Leibniz cohomology and the Chevalley–Eilenberg cohomology. As an application, we prove a conjecture stated by Pirashvili in [ 9].
Publisher
Oxford University Press (OUP)
Reference10 articles.
1. The algebra of rack and quandle cohomology;Clauwens;J. Knot Theory Ramifications,2011
2. From Poisson algebras to Gerstenhaber algebras;Kosmann-Schwarzbach;Ann. Inst. Fourier (Grenoble),1996
3. Cohomology of Lie algebras in the tensor category of linear maps;Kurdiani;Comm. Algebra,1999
4. $L_{\infty }$-algebra extensions of Leibniz algebras;Lavau
5. Une version non commutative des algèbres de Lie: les algèbres de Leibniz;Loday;Enseign. Math.,1993
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献