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Cohomology of restricted twisted Heisenberg Lie algebras
Part of:
Lie algebras and Lie superalgebras
Published online by Cambridge University Press: 06 November 2025
Abstract
Over an algebraically closed field 
$\mathbb F$ of characteristic 
$p \gt 0$, the restricted twisted Heisenberg Lie algebras are studied. We use the Hochschild–Serre spectral sequence relative to its Heisenberg ideal to compute the trivial cohomology. The ordinary 1- and 2-cohomology spaces are used to compute the restricted 1- and 2-cohomology spaces and describe the restricted one-dimensional central extensions, including explicit formulas for the Lie brackets and 
$-^{[p]}$-operators.
MSC classification
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- Research Article
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- © The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.
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