Abstract
Suppose that the underlying field is of characteristic different from 2 and 3. We first prove that the so-called stem deformations of a free presentation of a finite-dimensional Lie superalgebra L exhaust all the maximal stem extensions of L, up to equivalence of extensions. Then we prove that multipliers and covers always exist for a Lie superalgebra and they are unique up to superalgebra isomorphisms. Finally, we describe the multipliers, covers, and maximal stem extensions of Heisenberg superalgebras and model filiform Lie superalgebras.
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Acknowledgements
The authors thank the reviewers for their valuable suggestions. This work was supported in part by the National Natural Science Foundation of China (Grant No. 12061029), the Natural Science Foundation of Hainan Province (No. 120RC587), and the Natural Science Foundation of Heilongjiang Province (No. YQ2020A005).
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Liu, W., Miao, X. Multipliers, covers, and stem extensions for Lie superalgebras. Front. Math. China 16, 979–995 (2021). https://doi.org/10.1007/s11464-021-0907-8
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DOI: https://doi.org/10.1007/s11464-021-0907-8