Journal of Lie Theory

no. 4
On Lie Superalgebras with a Filiform Module as an Odd Part
Journal of Lie Theory, Volume 32 (2022) no. 4, pp. 917-936
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.
DOI: 10.5802/jolt.1259
Classification: 17A70, 17B05, 17B30
Keywords: Lie superalgebras, quadratic Lie superalgebras, double extensions, solvable, filiform 
@article{JOLT_2022_32_4_a1,
     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},
     doi = {10.5802/jolt.1259},
     zbl = {1521.17021},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1259/}
}
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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, Volume 32 (2022) no. 4, pp. 917-936. doi: 10.5802/jolt.1259

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