13 papers
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.…
On the Structure of Low-Dimensional Poisson Algebras over Arbitrary Fields
A. V. Petrov, O. O. Pypka
We investigate the structure of Poisson algebras of dimensions at most three over an arbitrary field. Our approach is based on the internal structure of the associated commutative…
Dedekind Poisson Algebras over Arbitrary Fields
A. I. Plakosh, O. O. Pypka
We study Poisson algebras in which every Poisson subalgebra is a Poisson ideal, called Dedekind Poisson algebras, over arbitrary fields and without any finite-dimensionality assump…
Leibniz rings: some basic and structural results
L. A. Kurdachenko, O. O. Pypka, M. M. Semko
In this paper, we study the fundamental properties of Leibniz rings. Special attention is given to the structure of Leibniz rings whose additive group is "small". The results obtai…
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 some relationships between the center and the derived subalgebra in Poisson (2-3)-algebras
P. Ye. Minaiev, O. O. Pypka, I. V. Shyshenko
One of the classic results of group theory is the so-called Schur theorem. It states that if the central factor-group of a group is finite, then its derived subgroup $…
On some relationships between the centers and the derived ideal in Leibniz 3-algebras
P. Ye. Minaiev, O. O. Pypka
One of the classic results of group theory is the so-called Schur theorem. It states that if the central factor-group of a group is finite, then its derived subgroup $…
On the automorphism groups of some nilpotent 3-dimensional Leibniz algebras
L. A. Kurdachenko, O. O. Pypka, M. M. Semko
Let be an algebra over a field with the binary operations and . Then is called a left Leibniz algebra if it satisfies the left Leibniz identity: $[[a,b],c]=[a,…
Automorphism groups of some 3-dimensional Leibniz algebras
L. A. Kurdachenko, O. O. Pypka, M. M. Semko
Let be an algebra over a field with the binary operations and . Then is called a left Leibniz algebra if it satisfies the left Leibniz identity: $[[a,b],c]=[a,…
On the inner structure of 3-dimensional Leibniz algebras
Leonid A. Kurdachenko, Oleksandr O. Pypka, Igor Ya. Subbotin
Let be an algebra over a field with the binary operations and . Then is called a left Leibniz algebra if for all .…
Relationships between the generalized central series of Leibniz algebras
Aleksandr A. Pypka
The purpose of this article is to show a close relationship between the generalized central series of Leibniz algebras. Some analogues of the classical group-theoretical theorems o…
On Leibniz algebras, whose subalgebras are either ideals or self-idealizing
Leonid A. Kurdachenko, Aleksandr A. Pypka, Igor Y. Subbotin
A subalgebra S of a Leibniz algebra L is called self-idealizing in L if it coincides with its idealizer IL(S). In this paper we study the structure of Leibniz algebras, whose subal…