Results 11 to 20 of about 670,256 (260)

On the derivations of Leibniz algebras of low dimension

Доповiдi Нацiональної академiї наук України, 2023
Let L be an algebra over a field F. Then L is called a left Leibniz algebra if its multiplication operations [×, ×] addition- ally satisfy the so-called left Leibniz identity: [[a,b],c] = [a,[b,c]] – [b,[a,c]] for all elements a, b, c Î L. In this paper,
L.A. Kurdachenko, M.M. Semko, V.S. Yashchuk   +2 more
doaj   +4 more sources

On the automorphism groups of some Leibniz algebras [PDF]

International Journal of Group Theory, 2023
We study the automorphism groups of finite-dimensional cyclic Leibniz algebras. In this connection, we consider the relationships between groups, modules over associative rings and Leibniz algebras.
Leonid Kurdachenko, Aleksand Pypka, Igor Subbotin   +2 more
doaj   +2 more sources

Leibniz Algebras and Lie Algebras [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2013
This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking ...
Geoffrey Mason, Gaywalee Yamskulna
doaj   +5 more sources

Solvable Leibniz Algebras with Filiform Nilradical [PDF]

, 2015
In this paper we continue the description of solvable Leibniz algebras whose nilradical is a filiform algebra. In fact, solvable Leibniz algebras whose nilradical is a naturally graded filiform Leibniz algebra are described in [6] and [8].
Camacho Santana, Luisa María, Masutova, K. K., Omirov, Bakhrom Abdazovich   +2 more
core   +3 more sources

Description of the automorphism groups of some Leibniz algebras

Researches in Mathematics, 2023
Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[,]$. Then $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in L$.
L.A. Kurdachenko, O.O. Pypka, M.M. Semko
doaj   +2 more sources

On Inner Derivations of Leibniz Algebras

Mathematics
Leibniz algebras are generalizations of Lie algebras. Similar to Lie algebras, inner derivations play a crucial role in characterizing complete Leibniz algebras.
Sutida Patlertsin, Suchada Pongprasert, Thitarie Rungratgasame   +2 more
doaj   +2 more sources

Cyclic Leibniz Algebras [PDF]

, 2014
Leibniz algebras generated by one element, called cyclic, provide simple and illuminating examples of many basic concepts. It is the purpose of this paper to illustrate this fact.
Kristin Bugg, Allison Hedges, Minji Lee, Daniel Scofield, S. McKay Sullivan   +4 more
openalex   +3 more sources

Automorphism groups of some non-nilpotent Leibniz algebras

Researches in Mathematics
Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[,]$. Then $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity: $[a,[b,c]]=[[a,b],c]+[b,[a,c]]$ for all $a,b,c\in L$. A linear transformation $f$ of $L$
L.A. Kurdachenko, P.Ye. Minaiev, O.O. Pypka   +2 more
doaj   +2 more sources

A characterization of nilpotent Leibniz algebras

Algebras and Representation Theory, 2012
W. A. Moens proved that a Lie algebra is nilpotent if and only if it admits an invertible Leibniz-derivation. In this paper we show that with the definition of Leibniz-derivation from W. A.
Fialowski, Alice, Khudoyberdiyev, A. Kh., Omirov, B. A.   +2 more
core   +3 more sources

Omni-Representations of Leibniz Algebras [PDF]

Communications in Mathematical Research, 2023
In this paper, first we introduce the notion of an omni-representation of a Leibniz algebra $g$ on a vector space $V$ as a Leibniz algebra homomorphism from $g$ to the omni-Lie algebra $gl(V)⊕V.$ Then we introduce the omni-cohomology theory associated to omni-representations and establish the relation between omni-cohomology groups and Loday-Pirashvili
Liu, Zhangju, Sheng, Yunhe
openaire   +3 more sources