On the role played by anticommutativity in Leibniz algebras

Abstract

Lie algebras are exactly the anticommutative Leibniz algebras. We conduct a brief analysis of the approach to Leibniz algebras which is based on the concept of anticenter (Lie-center) and antinilpotency (Lie nilpotentency).

On Leibniz algebras with maximal cyclic subalgebras

“…This approach turned out to be quite effective. We will not do any review of the results here, we just make links to surveys [6,11], and the papers [5,7,8,9,10,12,13,16,21].…”