Conjugacy of Cartan subalgebras of complex finite dimensional Leibniz algebras

@article{Omirov2006ConjugacyOC,
  title={Conjugacy of Cartan subalgebras of complex finite dimensional Leibniz algebras},
  author={B. A. Omirov},
  journal={Journal of Algebra},
  year={2006},
  volume={302},
  pages={887-896}
}
  • B. Omirov
  • Published 15 August 2006
  • Mathematics
  • Journal of Algebra
View PDF on arXiv
58 Citations
Highly Influential Citations
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Background Citations
18
Methods Citations
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Results Citations
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58 Citations

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Conjugacy of Cartan Subalgebras in Solvable Leibniz Algebras and Real Leibniz Algebras
We extend conjugacy results from Lie algebras to their Leibniz algebra generalizations. The proofs in the Lie case depend on anti-commutativity. Thus it is necessary to find other paths in the…
Cartan Subalgebras of Leibniz n-Algebras
The present article is devoted to the investigation of properties of Cartan subalgebras and regular elements in Leibniz n-algebras. The relationship between Cartan subalgebras and regular elements of…
Engel subalgebras of Leibniz algebras
Engel subalgebras of finite-dimensional Leibniz algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that a left Leibniz algebra, all of whose maximal…
Some radicals, Frattini and Cartan subalgebras of Leibniz n-algebras
Abstract In the present work, we introduce notions such as -solvability, - and -nilpotency and the corresponding radicals. We prove that these radicals are invariant under derivations of Leibniz…
Some Theorems on Leibniz Algebras
If U is a subnormal subalgebra of a finite-dimensional Leibniz algebra L and M is a finite-dimensional irreducible L-bimodule, then all U-bimodule composition factors of M are isomorphic. If U is a…
Leibniz algebras associated with some finite-dimensional representation of Diamond Lie algebra
In this paper we classify Leibniz algebras whose associated Lie algebra is four-dimensional Diamond Lie algebra 𝕯 and the ideal generated by squares of elements is represented by one of the…
Representations of Leibniz Algebras
In this paper we prove that every irredicuble representation of a Leibniz algebra can be obtained from irreducible representations of the semisimple Lie algebra from the Levi decomposition. We also…
REPRESENTATIONS OF LEIBNIZ ALGEBRAS
In this paper we prove that every irreducible representation of a Leibniz algebra can be obtained from irreducible representations of the semisimple Lie algebra from the Levi decomposition. We also…
On classification of complex filiform Leibniz algebras
In this paper we prove that in classifying of complex filiform Leibniz algebras, for which its naturally graded algebra is non-Lie algebra, it suffices to consider some special basis transformations.…
On Classification of Filiform Leibniz Algebras
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…
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References

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ABSTRACT Leibniz algebras that are noncommutative generalizations of Lie algebras are considered. Nilpotent and simple Leibniz algebras are investigated. The structure theory of finite-dimensional…
Crossed extensions of leibniz algebras
Crossed extensions of Leibniz algebras are studied, and an enlargement to eight terms of a five term exact and natural sequence for Leibniz cohomology is obtained. This eight term natural and exact…
The Second Leibniz Homology Group for Kac–Moody Lie Algebras
It is well known that the second homology group of any Kac–Moody Lie algebra and the Virasoro algebra is trivial. This is equivalent to saying that any Kac–Moody Lie algebra (or the Virasoro algebra)…
Leibniz homilogy of dialgebras of matrices
Ten-Term Exact Sequence of Leibniz Homology
Abstract We construct a ten-term exact sequence of low dimensional Leibniz homology associated to a short exact sequence of Leibniz algebras. As a consequence we obtain an eight-term exact sequence…
Homology and cohomology with coefficients, of an algebra over a quadratic operad
Homology and cohomology with coefficients, of an algebra over a quadratic operad
The aim of this paper is to give a definition of groups of homology and cohomology with coefficients, for an algebra over a quadratic operad in characteristic zero. Our work completes the works of…
Leibniz homology of dialgebras of matrices
A dialgebra D is a vector space with two associative operations -1, F satisfying three more relations. By setting [x, ~1 := x -I y y k x, any dialgebra gives rise to a Leibniz algebra. Here we…
Une version non commutative des algèbres de Lie : les algèbres de Leibniz
© Université Louis Pasteur (Strasbourg), 1993, tous droits réservés. L’accès aux archives de la série « Recherche Coopérative sur Programme no 25 » implique l’accord avec les conditions générales…
On Some Classes of Nilpotent Leibniz Algebras
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