2011
DOI: 10.1080/00927872.2010.489529
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Some Theorems on Leibniz Algebras

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Cited by 83 publications
(111 citation statements)
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“…In particular, Engel's theorem has been extended in [Ayupov and Omirov 1998;Barnes 2011;Patsourakos 2007]. In the second of these works, the classical Engel's theorem is used to give a short proof of the result for Leibniz algebras.…”
mentioning
confidence: 99%
“…In particular, Engel's theorem has been extended in [Ayupov and Omirov 1998;Barnes 2011;Patsourakos 2007]. In the second of these works, the classical Engel's theorem is used to give a short proof of the result for Leibniz algebras.…”
mentioning
confidence: 99%
“…It is interesting to note that the technique of reducing the problem to the special Lie algebra case significantly shortens the proof for the general Leibniz algebras case. This approach has been used in a number of situations [Barnes 2011]. We also note some standard consequences of this theorem.…”
Section: Conclusion and Open Questionsmentioning
confidence: 99%
“…In particular, Engel's theorem has been extended in [Ayupov and Omirov 1998;Barnes 2011;Patsourakos 2007]. In the second of these works, the classical Engel's theorem is used to give a short proof of the result for Leibniz algebras.…”
Section: Conclusion and Open Questionsmentioning
confidence: 99%
“…For example: In [5], [14], [15], the authors study nilpotent Leibniz n-algebras, nilpotent Lie and Leibniz algebras, nilpotent n-Lie algebras, respectively; D. W. Barnes discusses Engel subalgebras of Leibniz algebras in [3], and so on. In 1996, the concept of n-Lie superalgebras was first introduced by Yu.…”
Section: Introductionmentioning
confidence: 99%