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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

Yong Yang Open the ORCID record for Yong Yang [Opens in a new window]
Yong Yang*
Affiliation:
College of Mathematics and System Science, Xinjiang University, Urumqi, China (yangyong195888221@163.com)
*
*Corresponding author.
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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.

Keywords

central extension(restricted) cohomologyrestricted Lie algebratwisted Heisenberg algebra

MSC classification

Primary: 17B50: Modular Lie (super)algebras 17B56: Cohomology of Lie (super)algebras

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 12
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.

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