Results 221 to 230 of about 670,256 (260)

Leibniz n-algebras

Forum Mathematicum, 2002
The paper provides foundational material for the construction of free Leibniz \(n\)-algebras and an interpretation of Leibniz \(n\)-algebra cohomology in terms of Quillen cohomology. Motivated by generalizations of Lie algebra structures to settings with \(n\)-ary operations, the authors define a Leibniz \(n\)-algebra to be a vector space \(\mathcal{L}\
Casas, J. M., Loday, J.-L., Pirashvili, T.   +2 more
openaire   +3 more sources

Local and 2-local automorphisms of solvable Leibniz algebras with abelian and model nilradicals

Quaestiones Mathematicae. Journal of the South African Mathematical Society, 2023
In the paper, we describe the automorphisms on the solvable Leibniz algebras with the model or abelian nilradicals, whose complementary spaces are equal to two and one, respectively.
Iqboljon Karimjanov, S. Umrzaqov, B. Yusupov   +2 more
semanticscholar   +1 more source

Cohomology of Leibniz Algebras

Jahresbericht der Deutschen Mathematiker-Vereinigung, 2023
The paper under review is a survey of recent results on the cohomology of Leibniz algebras which are due to the author and the reviewer [J. Algebra 569, 276--317 (2021; Zbl 1465.17006); Indag. Math., New Ser. 35, No. 1, 87--113 (2024; Zbl 1543.17003)].
openaire   +2 more sources

From relative Rota-Baxter operators and relative averaging operators on Lie algebras to relative Rota-Baxter operators on Leibniz algebras: a uniform approach

Mathematical Research Letters, 2023
In this paper, first we construct two subcategories (using symmetric representations and antisymmetric representations) of the category of relative Rota-Baxter operators on Leibniz algebras, and establish the relations with the categories of relative ...
Rong Tang, Y. Sheng, F. Wagemann
semanticscholar   +1 more source

Leibniz algebras in characteristic

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2001
The paper under review presents a definition of a restricted Leibniz algebra \(Q\) in characteristic \(p\), and then presents a condition for the non-vanishing of the Leibniz cohomology of \(Q\). In particular, let \(k\) be an algebraically closed field of characteristic \(p > 0\), and let \(Q\) be a (left) Leibniz algebra over \(k\).
Dzhumadil'daev, Askar S., Abdykassymova, Saule A.   +1 more
openaire   +2 more sources

The geometric classification of symmetric Leibniz algebras

Communications in Mathematics
This paper is devoted to the complete geometric classification of complex 5-dimensional solvable symmetric Leibniz algebras. As a corollary, we have the complete geometric classification of complex 5-dimensional symmetric Leibniz algebras.
Renato Fehlberg Junior, I. Kaygorodov, A. Saydaliyev   +2 more
semanticscholar   +1 more source

Anti-Leibniz algebras: A non-commutative version of mock-Lie algebras

Journal of Geometry and Physics
Leibniz algebras are non skew-symmetric generalization of Lie algebras. In this paper we introduce the notion of anti-Leibniz algebras as a"non commutative version"of mock-Lie algebras. Low dimensional classification of such algebras is given.
S. Braiek, T. Chtioui, S. Mabrouk
semanticscholar   +1 more source

From Leibniz Algebras to Lie 2-algebras

Algebras and Representation Theory, 2015
The authors construct a Lie 2-algebra associated to every Leibniz algebra via the skew-symmetrization.
Sheng, Yunhe, Liu, Zhangju
openaire   +2 more sources

VARIETIES OF METABELIAN LEIBNIZ ALGEBRAS

Journal of Algebra and Its Applications, 2002
In this paper we commence the systematic study of T-ideals of the free Leibniz algebra or, equivalently, varieties of Leibniz algebras, over a field of characteristic 0. We give a description of the free metabelian (i.e. solvable of class 2) Leibniz algebras, a complete list of all left-nilpotent of class 2 varieties and the asymptotic description of ...
Drensky, Vesselin, Piacentini Cattaneo, Giulia Maria   +1 more
openaire   +2 more sources

R-Matrices for Leibniz Algebras

Letters in Mathematical Physics, 2003
The authors introduce \(R\)-matrices for Leibniz algebras as a direct generalization of the classical \(R\)-matrices. The linear mapping \(R_{\pm}: L\to L\) of a Leibniz algebra \(L\) is called an \(R_{\pm}\)-matrix if the new bilinear operator defined by \([X,Y]_{R_{\pm}}=[RX,Y]\pm [X,RY]\), \(X,Y\in L\), satisfies the Jacobi-Leibniz identity.
Felipe, Raúl, López-Reyes, Nancy, Ongay, Fausto   +2 more
openaire   +1 more source