Leibniz algebras
Leibniz algebras with absolute maximal Lie subalgebras
... Leibniz algebras form a semi-abelian category [7, 14], denoted by Leib , whose morphisms are linear maps that preserve the Leibniz ...The Leibniz identity above generalizes the Jacobi identity ...
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Derivations of Some Filiform Leibniz Algebras
... the present paper we study the derivation algebras of low- dimensional Leibniz algebras. The outline of the paper is as follows. Section 1 is a brief introduction. Section 2 we give derivations of ...
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Some Criteria for Solvable and Supersolvable Leibniz Algebras.
... non-Lie Leibniz algebras are the cyclic Leibniz ...cyclic algebras [ McA14 ] . The cyclic Leibniz algebras have been classified over the complex numbers in [ SS14 ] ...
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The Generalized Ideal Index and CAP*-subalgebras of Leibniz Algebras.
... Lie algebras, the ideal index provides useful results related to Lie algebra ...to Leibniz algebras by Turner in [ 16 ] ...to Leibniz algebras along with properties that still hold in ...
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Frattini Properties of Leibniz Algebras.
... of Leibniz algebras generated by one element, called cyclic Leibniz ...Cyclic Leibniz algebras provide counterexamples for many extensions of results from Lie algebras to ...
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Formations of Leibniz Algebras.
... solvable Leibniz algebras, whereas saturated and non-saturated formations may include Leibniz algebras which are not solvable as seen in Example ...solvable Leibniz algebras S in ...
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Conjugacy and Other Results in Leibniz Algebras.
... a Leibniz algebra, denoted φ( L ) ...φ-free Leibniz algebra L , which is minimally not in a formation of solvable Leibniz ...a Leibniz algebra from a Lie ...of algebras, where X is a ...
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Classification of 5-Dimensional Complex Nilpotent Leibniz Algebras.
... nilpotent Leibniz algebras were first studied by Loday ...nilpotent Leibniz algebras of dimension n ≤ ...nilpotent Leibniz algebras in [3] and ...
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On some Leibniz algebras, having small dimension
... Leibniz algebras appeared first in the papers of ...to Leibniz algebras ...these algebras and used the term Leibniz algebras since it was Gottfried Wilhelm Leibniz ...
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On Derivations of Leibniz Algebras.
... of Leibniz algebras in 1993, researchers have been working to determine which properties of Lie algebras can be extended to Leibniz ...for Leibniz algebras are analogs of Lie’s ...
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On the structure of Leibniz algebras whose subalgebras are ideals or core-free
... a Leibniz algebra (more precisely, a left Leibniz algebra) if it satisfies the Leibniz identity: [[a, b], c] = [a, [b, c]] − [b, [a, c]] for all a, b, c ∈ ...L. Leibniz algebras are ...
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On the anticommutativity in Leibniz algebras
... between Leibniz algebras and Lie algebras consists in the absence of anticommuta- tivity, we naturally come to the next object in Leibniz ...
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Supersolvable Leibniz Algebras.
... of algebras if whenever all n generated subalgebras have the property, then the algebra has the ...Lie algebras and Leibniz algebras for classes that are solvable, supersolvable, nilpotent and ...
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Complemented Leibniz Algebras.
... solvable Leibniz algebras following Towers’ work from ...complemented Leibniz algebras following Towers’ lead in Lie ...solvable Leibniz algebras and another for solvable ...
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Leibniz A algebras
... such algebras are sometimes called right Leibniz algebras, and there is a corresponding notion of left Leibniz ...a Leibniz algebra and every Leibniz algebra satisfy- ing [x, x] ...
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Subinvariance and Supersolvability of Leibniz Algebra
... Lie algebras [ O’C00 ] . Leibniz algebras are a generalization of Lie .... Leibniz algebras satisfy all definitions of Lie algebras except the antisymmetry ...right ...
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Some aspects of Leibniz algebra theory
... these algebras and used the term Leibniz algebras since it was Gottfried Wilhelm Leibniz who discovered and proved the Leibniz rule for differentiation of ...these algebras by ...
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q Schur algebras and quantized enveloping algebras
... The v-Schur algebra as a subspace of tensor matrix space We have seen in the above sections that the classical Schur algebra Sn, r embeds in T"Mn in a natural way compatible with the U-m[r] ...
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Elementary Lie Algebras and Lie A Algebras
... such algebras for which the nilpotent subalgebra N in the Iwasawa decomposition of L is abelian are sl(2, R ) and so(n, 1) (n > ...the algebras described in ...
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Generalizations of fractional q Leibniz formulae and applications
... 4 A q-extension of the Leibniz rule via Weyl-type of a q-derivative operator In this section, we prove that the q-expansion in () can be derived for any α ∈ R. The proof we introduce is completely different from ...
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