Classification of some nilpotent class of leibniz superalgebras

Camacho, L.M.; Gómez, José Manuel; Navarro, R.M.; Omirov, B. A.

doi:10.1007/s10114-010-8358-2

Cited by 11 publications

(15 citation statements)

References 9 publications

(5 reference statements)

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“…. ,m s ) either n 1 n − 1 or m 1 = m were already classified in [3][4][5][6], we shall reduce our investigation to the case of the characteristic sequence (n 1 , . .…”

Section: Preliminariesmentioning

confidence: 99%

“…For the completeness of the statement below we recall the classifications of the papers [3][4][5][6]8].…”

Section: Preliminariesmentioning

confidence: 99%

“…Using these products for the corresponding products in the Leibniz algebra L 0 with the basis 3,4 x 4 + γ 3,5 x 5 + · · · + γ 3,n x n . …”

Section: The Case Of Both Generators Lie In Lmentioning

confidence: 99%

“…. ,m s ) (n 1 n − 2 and m 1 m − 1) and nilindex n + m. Recall, that such superalgebras for n 1 n − 1 or m 1 = m have been already classified in works [3][4][5][6]. Namely, we prove that a Leibniz superalgebra with characteristic sequence equal to (n 1 , .…”

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confidence: 95%

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The classification of Leibniz superalgebras of nilindex n+m (m≠0)

2010

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In this paper we investigate the description of the complex Leibniz superalgebras with nilindex n + m, where n and m (m = 0) are dimensions of even and odd parts, respectively. In fact, such superalgebras with characteristic sequence equal to (n 1 , . . . ,n k | m 1 , . . . ,m s ) (where n 1 + · · · + n k = n, m 1 + · · · + m s = m) for n 1 n − 1 and (n 1 , . . . ,n k | m) were classified in works by Ayupov et al. (2009) [3], Camacho et al. (2010) [4], Camacho et al. (in press) [5], Camacho et al. (in press) [6]. Here we prove that in the case of (n 1 , . . . ,n k | m 1 , . . . ,m s ), where n 1 n − 2 and m 1 m − 1 the Leibniz superalgebras have nilindex less than n + m. Thus, we complete the classification of Leibniz superalgebras with nilindex n + m.

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“…. ,m s ) either n 1 n − 1 or m 1 = m were already classified in [3][4][5][6], we shall reduce our investigation to the case of the characteristic sequence (n 1 , . .…”

Section: Preliminariesmentioning

confidence: 99%

“…For the completeness of the statement below we recall the classifications of the papers [3][4][5][6]8].…”

Section: Preliminariesmentioning

confidence: 99%

“…Using these products for the corresponding products in the Leibniz algebra L 0 with the basis 3,4 x 4 + γ 3,5 x 5 + · · · + γ 3,n x n . …”

Section: The Case Of Both Generators Lie In Lmentioning

confidence: 99%

mentioning

confidence: 95%

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The classification of Leibniz superalgebras of nilindex n+m (m≠0)

2010

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“…Taking into account the results of the papers [6] and [9], where some cases of nilpotent Leibniz superalgebras were described, in this work we investigate the rest cases. Thus, we complete the description of Leibniz superalgebras with characteristic sequence C(L) = (n | m 1 , .…”

Section: Introductionmentioning

confidence: 99%