Geodesic
On Lie Superalgebras with a Filiform Module as an Odd Part
Journal of Lie theory, Tome 32 (2022) no. 4, pp. 917-936
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The aim of this work is on one hand to characterise in any even dimension, via double extensions, a very special family of quadratic Lie superalgebras ${\mathfrak g}={\mathfrak g}_{\bar 0}\oplus {\mathfrak g}_{\bar 1}$ such that ${\mathfrak g}_{\bar 1}$ is a filiform ${\mathfrak g}_{\bar 0}$-module (filiform type). On the other hand, we show that the study of quadratic Lie superalgebras of filiform type can be reduced to those that are solvable. Moreover, we obtain an inductive description of solvable quadratic Lie superalgebras of filiform type via both double extensions and odd double extensions of quadratic ones.
Classification : 17A70, 17B05, 17B30
Mots-clés : Lie superalgebras, quadratic Lie superalgebras, double extensions, solvable, filiform 
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     author = {E. Barreiro and S. Benayadi and R. M. Navarro and J. M. S\~A{\textexclamdown}nchez},
     title = {On {Lie} {Superalgebras} with a {Filiform} {Module} as an {Odd} {Part}},
     journal = {Journal of Lie theory},
     pages = {917--936},
     year = {2022},
     volume = {32},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2022_32_4_JLT_2022_32_4_a1/}
}
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E. Barreiro; S. Benayadi; R. M. Navarro; J. M. Sánchez. On Lie Superalgebras with a Filiform Module as an Odd Part. Journal of Lie theory, Tome 32 (2022) no. 4, pp. 917-936. http://geodesic.mathdoc.fr/item/JLT_2022_32_4_JLT_2022_32_4_a1/