Derivations of finite-dimensional modular Lie superalgebras $ \overline{K}(n, m) $

Dan Mao; Keli Zheng; Dan Mao; Keli Zheng

doi:10.3934/era.2023217

Electronic Research Archive

2023, Volume 31, Issue 7: 4266-4277. doi: 10.3934/era.2023217

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Theory article

Derivations of finite-dimensional modular Lie superalgebras $ \overline{K}(n, m) $

Dan Mao ^1,2,
Keli Zheng ^{1
,
,}

1.
Department of Mathematics, School of Science, Northeast Forestry University, Harbin 150040, China
2.
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Received: 28 February 2023 Revised: 08 May 2023 Accepted: 22 May 2023 Published: 01 June 2023

This paper is aimed at determining the derivation superalgebra of modular Lie superalgebra $ \overline{K}(n, m) $. To that end, we first describe the $ \mathbb{Z} $-homogeneous derivations of $ \overline{K}(n, m) $. Then we obtain the derivation superalgebra $ Der(\overline{K}) $. Finally, we partly determine the derivation superalgebra $ Der(K) $ by virtue of the invariance of $ K(n, m) $ under $ Der(\overline{K}) $.
- Lie superalgebra,
- modular Lie superalgebra,
- derivation superalgebra,
- associative superalgebra,
- contact type
Citation: Dan Mao, Keli Zheng. Derivations of finite-dimensional modular Lie superalgebras $ \overline{K}(n, m) $[J]. Electronic Research Archive, 2023, 31(7): 4266-4277. doi: 10.3934/era.2023217

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Abstract

This paper is aimed at determining the derivation superalgebra of modular Lie superalgebra $ \overline{K}(n, m) $. To that end, we first describe the $ \mathbb{Z} $-homogeneous derivations of $ \overline{K}(n, m) $. Then we obtain the derivation superalgebra $ Der(\overline{K}) $. Finally, we partly determine the derivation superalgebra $ Der(K) $ by virtue of the invariance of $ K(n, m) $ under $ Der(\overline{K}) $.

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