Some notes on the second homology of Leibniz algebras

ABSTRACT

Some properties of the second homology and cover of Leibniz algebras are established. By constructing a stem cover, the second Leibniz homology and cover of abelian, Heisenberg Lie algebras and cyclic Leibniz algebras are described. Also, for the dimension of a non-cyclic nilpotent Leibniz algebra L, we obtain dim(HL₂(L))≥2.

KEYWORDS:

• Cover
• Leibniz algebras
• Leibniz homology

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 17A32