Results 151 to 160 of about 455 (185)

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
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Quadratic Leibniz Algebras

Journal of Lie Theory, 2014
Left (or right) Leibniz algebras endowed with symmetric non-degenerate and associative bilinear forms (called quadratic Leibniz algebras) are investigated. In particular, we prove that left (resp. right) Leibniz algebras that carry this structure are also right (resp. left) Leibniz algebras.
Benayadi, Saïd, Hidri, Samiha
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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
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On some “minimal” Leibniz algebras

Journal of Algebra and Its Applications, 2017
The aim of this paper is to describe some “minimal” Leibniz algebras, that are the Leibniz algebras whose proper subalgebras are Lie algebras, and the Leibniz algebras whose proper subalgebras are abelian.
Chupordia, V. A., Kurdachenko, L. A., Subbotin, I. Ya.   +2 more
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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
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ON REPRESENTATIONS OF SYMMETRIC LEIBNIZ ALGEBRAS

Glasgow Mathematical Journal, 2019
AbstractWe give a new and useful approach to study the representations of symmetric Leibniz algebras. Using this approach, we obtain some results on the representations of these algebras.
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On Classification of Filiform Leibniz Algebras

Algebra Colloquium, 2015
In this work we prove that in classifying of filiform Leibniz algebras whose naturally graded algebra is a non-Lie algebra, it suffices to consider some special basis transformations. Moreover, we derive a criterion for two such Leibniz algebras to be isomorphic in terms of such transformations.
Gómez, J. R., Omirov, B. A.
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On Leibniz Algebras

1998
This work is devoted to study of comparatively new algebraic object - Leibniz algebras, introduced by Loday [1], as a “non commutative” analogue of Lie algebras.
Sh. A. Ayupov, B. A. Omirov
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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
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Weak Leibniz Algebras

Mathematical Notes
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