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Darabi, Hamid; Saeedi, Farshid; Eshrati, Mehdi

doi:10.1016/j.geomphys.2016.07.001

Cited by 8 publications

(2 citation statements)

References 14 publications

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“…In he same year, 2016, Schneider and Usefi classified p-nilpotent restricted Lie algebras of dimension at most 4 [229] and L. Cagliero and F. Szechtman the linked indecomposable modules of a family of solvable Lie algebras over an arbitrary field of characteristic 0 [48]. Besides, in [73], H. Darabi, F. Saeedi and M. Eshrati dealt with capable n-Lie algebras and the classification of nilpotent n-Lie algebras with s(A) = 3 and A.S. Hegazi, H. Abdelwahab and A.J. Calderon Martin classified the n-dimensional non-Lie Malcev algebras with (n − 4)-dimensional annihilator [121].…”

Section: Nilpotent Lie Algebras: Classificationmentioning

confidence: 99%

The trascendence of Kac-Moody algebras

Fernández-Ternero

Valdés

2021

Filomat

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With the main objective that it can be consulted by all researchers, mainly young people, interested in the study of the Kac-Moody algebras and their applications, this paper aims to present the past and present state-of-the-art developments and results on these algebras at various levels of analysis and fields of application in different disciplines. Indeed, lot of references in the literature on these algebras are analyzed and a study of the most relevant topics regarding them is shown.

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Section: Nilpotent Lie Algebras: Classificationmentioning

confidence: 99%

The trascendence of Kac-Moody algebras

Fernández-Ternero

Valdés

2021

Filomat

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“…One can define the solvable ideal of a Filippov algebra, simple and semisimple Filippov algebras, etc., see [28]. Some properties of nilpotent Filippov algebras were studied in [15,16,21]. Two cohomological properties of semisimple Lie algebras also hold in the Filippov algebras case.…”

Section: The Variety Of Filippov Algebrasmentioning

confidence: 99%

Degenerations of Filippov algebras

Kaygorodov

Volkov

2020

Journal of Mathematical Physics

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Yury Volkov (wolf86 666@list.ru).We consider the variety of Filippov (n-Lie) algebra structures on an (n + 1)-dimensional vector space. The group GL n (K) acts on it, and we study the orbit closures with respect to the Zariski topology. This leads to the definition of Filippov algebra degenerations. We present some fundamental results on such degenerations, including trace invariants and necessary degeneration criteria. Finally, we classify all orbit closures in the variety of complex (n + 1)-dimensional Filippov n-ary algebras.

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On Classification of (n+1)-Dimensional n-Hom-Lie Algebras with Nilpotent Twisting Maps

Kitouni,

Silvestrov

2023

Springer Proceedings in Mathematics &Amp; Statistics

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Capable n-Lie algebras and the classification of nilpotent n-Lie algebras with s(

Cited by 8 publications

References 14 publications

The trascendence of Kac-Moody algebras

The trascendence of Kac-Moody algebras

Degenerations of Filippov algebras

On Classification of (n+1)-Dimensional n-Hom-Lie Algebras with Nilpotent Twisting Maps

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