Journal of Lie Theory

no. 2
Classification of Finite Dimensional Nilpotent Lie Superalgebras by their Multipliers
Journal of Lie Theory, Volume 31 (2021) no. 2, pp. 439-458
Let $L$ be a nilpotent Lie superalgebra of dimension $(m\mid n)$ and $$ s(L) = \frac{1}{2}[(m + n - 1)(m + n -2)]+ n+ 1 - \dim \mathcal{M}(L), $$ where $\mathcal{M}(L)$ denotes the Schur multiplier of $L$. Here $s(L)\geq 0$ and the structure of all non-abelian nilpotent Lie superalgebras with $s(L)=0$ is known from a previous publication of the author [{\em Multipliers of nilpotent Lie superalgebras}, Comm. Algebra 47/2 (2019) 689--705]. This paper is devoted to obtain all nilpotent Lie superalgebras $L$ when $s(L) \leq 2$. Further, we apply those results to list all non-abelian nilpotent Lie superalgebras $L$ with $ t(L) \leq 4$.
DOI: 10.5802/jolt.1179
Classification: 17B30, 17B05
Keywords: Nilpotent Lie superalgebra, multiplier, special Heisenberg Lie superalgebra 
@article{JOLT_2021_31_2_a7,
     author = {S. Nayak},
     title = {Classification of {Finite} {Dimensional} {Nilpotent} {Lie} {Superalgebras} by their {Multipliers}},
     journal = {Journal of Lie Theory},
     pages = {439--458},
     year = {2021},
     volume = {31},
     number = {2},
     doi = {10.5802/jolt.1179},
     zbl = {1492.17013},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1179/}
}
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S. Nayak. Classification of Finite Dimensional Nilpotent Lie Superalgebras by their Multipliers. Journal of Lie Theory, Volume 31 (2021) no. 2, pp. 439-458. doi: 10.5802/jolt.1179

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