Results 91 to 100 of about 40,026 (194)
On Leibniz algebras, whose subideals are ideals
Доповiдi Нацiональної академiї наук УкраїниWe obtain a description of solvable Leibniz algebras, whose subideals are ideals. A description of certain types of Leibniz T-algebras is also obtained. In particular, it is established that the structure of Leibniz T-algebras essentially depends on the
L.A. Kurdachenko +2 more
doaj +1 more source
MathematicsWe introduce para-associative algebroids as vector bundles whose sections form a ternary algebra with a generalised form of associativity. We show that a necessary and sufficient condition for local triviality is the existence of a differential ...
Andrew James Bruce
doaj +1 more source
Steinberg–Leibniz algebras and superalgebras
Journal of Algebra, 2005 The Steinberg Lie algebra \({\mathfrak s}{\mathfrak t}(n,A)\), \(n\geq 3\), over a unital associative algebra \(A\) is the universal central extension of the matrix Lie algebra \({\mathfrak s}{\mathfrak l}(n,A)\), and the Leibniz algebra \({\mathfrak s}{\mathfrak t}{\mathfrak l}(n,A)\) has a similar property in the category of Leibniz algebras.
openaire +2 more sources
A rigid Leibniz algebra with non-trivial HL^2
, 2019 In this article, we generalize Richardson's example of a rigid Lie algebra with non-trivial $H^2$ to the Leibniz setting. Namely, we consider the hemisemidirect product ${\mathfrak h}$ of a semidirect product Lie algebra $M_k\rtimes{\mathfrak g}$ of a ...
Omirov, Bakhrom, Wagemann, Friedrich
core
Almost-reductive and almost-algebraic Leibniz algebra
International Electronic Journal of AlgebraThis paper examines whether the concept of an almost-algebraic Lie algebra developed by Auslander and Brezin in [J. Algebra, 8(1968), 295-313] can be introduced for Leibniz algebras. Two possible analogues are considered: almost-reductive and almost-algebraic Leibniz algebras.
openaire +4 more sources
2-recognizeable classes of Leibniz algebras
Journal of Algebra, 2015 We show that for fields that are of characteristic 0 or algebraically closed of characteristic greater than 5, that certain classes of Leibniz algebras are 2-recognizeable. These classes are solvable, strongly solvable and super solvable. These results hold in Lie algebras and in general for groups.
Tiffany Burch +5 more
openaire +2 more sources
, 2008 2000 Mathematics Subject Classification: Primary 17A32, Secondary 17D25. An algebra (A,ο) is called Leibniz if aο(bοc) = (a ο b)ο c-(a ο c) ο b for all a,b,c ∈ A. We study identities for the algebras A(q) = (A,οq), where a οq b = a ο b+q b ο a is the q-commutator. Let Char K ≠ 2,3. We show that the class of q-Leibniz algebras is defined by one identity
openaire +2 more sources
ON LEVI’S THEOREM FOR LEIBNIZ ALGEBRAS [PDF]
Bulletin of the Australian Mathematical Society, 2011 AbstractA Lie algebra over a field of characteristic 0 splits over its soluble radical and all complements are conjugate. I show that the splitting theorem extends to Leibniz algebras but that the conjugacy theorem does not.
openaire +3 more sources
Solvable Leibniz algebras with NFn⊕ Fm1$\begin{array}{} F_{m}^{1} \end{array} $ nilradical
Open Mathematics, 2017 All finite-dimensional solvable Leibniz algebras L, having N = NFn⊕ Fm1$\begin{array}{} F_{m}^{1} \end{array} $ as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described.
Camacho L.M. +3 more
doaj +1 more source
Communications in AlgebraThe notion of pre-Leibniz algebras was recently introduced in the study of Rota-Baxter operators on Leibniz algebras. In this paper, we first construct a graded Lie algebra whose Maurer-Cartan elements are pre-Leibniz algebras. Using this characterization, we define the cohomology of a pre-Leibniz algebra with coefficients in a representation.
openaire +2 more sources