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

JOURNAL OF ALGEBRA

卷:324

Article

Gomez, J. R.²  Khudoyberdiyev, A. Kh.¹  Omirov, B. A.¹ 

[1] Acad Uzbekistan, Inst Math & Informat Technol, Tashkent 100125, Uzbekistan

[2] Univ Seville, Dpto Matemat Aplicada 1, E-41012 Seville, Spain

关键词: Lie superalgebras;    Leibniz superalgebras;    Nilindex;    Characteristic sequence;    Natural gradation;   

DOI  :  10.1016/j.jalgebra.2010.08.004

来源: Elsevier

【 摘 要 】

In this paper we investigate the description of the complex Leibniz superalgebras with nilindex n + m, where n and m (m not equal 0) are dimensions of even and odd parts, respectively. In fact, such superalgebras with characteristic sequence equal to (n(1), ... , n(k) vertical bar 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) vertical bar 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) vertical bar 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. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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