5 papers
On nilpotency in pre - Lie algebras
Leonid Kurdachenko, Igor Subbotin
The authors consider several variants of the notion of nilpotency in pre-Lie algebras and investigate the properties of nilpotent ideals.
Derivation Algebras of Three-Dimensional Leibniz Algebras: A Complete Description
Leonid A. Kurdachenko, Oleksandr O. Pypka, Mykola M. Semko
Derivation algebras are natural structural invariants of Leibniz algebras. In a number of earlier papers, derivations were described for several classes of one-generated, nilpotent…
Automorphism Groups of Three-Dimensional Leibniz Algebras: A Complete Description
Leonid A. Kurdachenko, Oleksandr O. Pypka, Mykola M. Semko
Automorphism groups are among the most natural structural invariants of an algebra, and their explicit determination is a basic problem in the structure theory of Leibniz algebras.…
Some three-dimensional non-nilpotent Leibniz algebras: automorphism groups
Leonid A. Kurdachenko, Oleksandr O. Pypka, Igor Ya. Subbotin
The article presents the structure of the automorphism groups of two types of non-nilpotent Leibniz algebras with a dimension of 3.
On a Generalization of Baer Theorem
L. A. Kurdachenko, J. Otal, I. YA. Subbotin
R. Baer has proved that if the factor-group G/ζ_{n}(G) of a group G by the member ζ_{n}(G) of its upper central series is finite (here n is a positive integer) then the member γ_{n…