Simple Filippov superalgebras of type~$B(m,n)$
Algebra i logika, Tome 47 (2008) no. 2, pp. 240-261.

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This account is a first step toward a classification of finite-dimensional simple Filippov superalgebras over an algebraically closed field of characteristic 0. Here, $n$-ary Filippov superalgebras with nonzero even and odd parts are treated for the case $n\geqslant3$.
Keywords: Filippov superalgebra, algebraically closed field of characteristic 0.
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A. P. Pozhidaev. Simple Filippov superalgebras of type~$B(m,n)$. Algebra i logika, Tome 47 (2008) no. 2, pp. 240-261. http://geodesic.mathdoc.fr/item/AL_2008_47_2_a6/

[1] Yu. Daletskii, V. Kushnirevich, “Inclusion of Nambu-Takhtajan algebra in formal differential geometry structure”, Dop. NAN Ukr., 1996, no. 4, 12–18 | MR

[2] V. T. Filippov, “$n$-lievy algebry”, Sib. matem. zh., 26:6 (1985), 126–140 | MR | Zbl

[3] J. Grabowski, G. Marmo, “On Filippov algebroids and multiplicative Nambu–Poisson structures”, Differ. Geom. Appl., 12:1 (2000), 35–50 | DOI | MR | Zbl

[4] A. P. Pojidaev, “Enveloping algebras of Filippov algebras”, Commun. Algebra, 31:2 (2003), 883–900 | DOI | MR | Zbl

[5] A. P. Pojidaev, “Solvability of finite-dimensional commutative $n$-ary Leibniz algebras of characteristic 0”, Commun. Algebra, 31:1 (2003), 197–215 | DOI | MR | Zbl

[6] Ling Wuxue, On the structure of $n$-Lie algebras, Thesis, Siegen Univ.–GHS, Siegen, 1993, 61 pp. | Zbl

[7] A. P. Pojidaev, “On simple Filippov superalgebras of type $B(0,n)$”, J. Algebra Appl., 2:3 (2003), 335–349 | DOI | MR | Zbl

[8] A. P. Pojidaev, P. Saraiva, “On simple Filippov superalgebras of type $B(0,n)$. II”, Portugaliae Math. (N.S.) (to appear)

[9] V. G. Kac, “Lie superalgebras”, Adv. Math., 26:1 (1977), 8–96 | DOI | MR | Zbl

[10] V. Kac, “Representations of classical Lie superalgebras”, Differ. geom. Meth. math. Phys. II, Proc. (Bonn, 1977), Lect. Notes Math., 676, 1978, 597–626 | MR | Zbl

[11] N. Jacobson, Lie algebras, Intersci. Tracts Pure Appl. Math., 10, Intersci. Publ. (a Division of John Wiley and Sons), New York–London, 1962 | MR | Zbl