A characterization of finite dimensional nilpotent Filippov algebras

Darabi, Hamid; Saeedi, Farshid; Eshrati, Mehdi

doi:10.1016/j.geomphys.2015.12.007

Cited by 15 publications

(7 citation statements)

References 16 publications

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“…So, we conclude β i,j,k = 0 for each 1 ≤ i < j < k ≤ 6, (i, j, k) = (1, 2, 3) , (4, 5, 6). Thus 1 ≤ i < j < k ≤ 6, (i, j, k) = (1, 2, 3), (4,5,6). Now, by choosing J = e 8 , we have dim (A/J ) 2 = 1.…”

Section: Classification Of (N+5)-dimensional Nilpotent N-lie Algebras...mentioning

confidence: 99%

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On classification of (n+5)-dimensional nilpotent n-Lie algebra of class two

Hoseini,

Saeedi,

Darabi

2018

Preprint

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Section: Classification Of (N+5)-dimensional Nilpotent N-lie Algebras...mentioning

confidence: 99%

“…In this case, according to the structure of A/I , we have α 0 = α i,j,k = 0. Therefore, the brackets of A are as follows: (4,5,6) . According to the above brackets and special Heisenberg n-Lie algebra, the above algebra is isomorphic to H (3, 1) ⊕ F (3).…”

Section: Classification Of (N+5)-dimensional Nilpotent N-lie Algebras...mentioning

confidence: 99%

On classification of (n+5)-dimensional nilpotent n-Lie algebra of class two

Hoseini,

Saeedi,

Darabi

2018

Preprint

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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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“…Theorem 3.1 [18]. Let A be a nilpotent n-Lie algebra of dimension d ¼ n þ k for 3 ≤ k ≤ n þ 1 such that A 2 ¼ Z ðAÞ and dimA2 ¼ 2.…”

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On classification of (n + 6)-dimensional nilpotent n-Lie algebras of class 2 with n ≥ 4

Jamshidi

Saeedi

Darabi

2020

AJMS

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PurposeThe purpose of this paper is to determine the structure of nilpotent (n+6)-dimensional n-Lie algebras of class 2 when n≥4.Design/methodology/approachBy dividing a nilpotent (n+6)-dimensional n-Lie algebra of class 2 by a central element, the authors arrive to a nilpotent (n+5) dimensional n-Lie algebra of class 2. Given that the authors have the structure of nilpotent (n+5)-dimensional n-Lie algebras of class 2, the authors have access to the structure of the desired algebras.FindingsIn this paper, for each n≥4, the authors have found 24 nilpotent (n+6) dimensional n-Lie algebras of class 2. Of these, 15 are non-split algebras and the nine remaining algebras are written as direct additions of n-Lie algebras of low-dimension and abelian n-Lie algebras.Originality/valueThis classification of n-Lie algebras provides a complete understanding of these algebras that are used in algebraic studies.

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A characterization of finite dimensional nilpotent Filippov algebras

Cited by 15 publications

References 16 publications

On classification of (n+5)-dimensional nilpotent n-Lie algebra of class two

On classification of (n+5)-dimensional nilpotent n-Lie algebra of class two

Degenerations of Filippov algebras

On classification of (n + 6)-dimensional nilpotent n-Lie algebras of class 2 with n ≥ 4

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