On the Cohomology of Restricted Heisenberg Lie Algebras

Tyler J. Evans; Alice Fialowski; Yong Yang

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arXiv · 2402.14249

On the Cohomology of Restricted Heisenberg Lie Algebras

Tyler J. Evans·Alice Fialowski·Yong Yang

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Abstract

We show that the Heisenberg Lie algebras over a field $\mathbb{F}$ of characteristic $p>0$ admit a family of restricted Lie algebras, and we classify all such non-isomorphic restricted Lie algebra structures. We use the ordinary 1- and 2-cohomology spaces with trivial coefficients to compute the restricted 1- and 2-cohomology spaces of these restricted Heisenberg Lie algebras. We describe the restricted 1-dimensional central extensions, including explicit formulas for the Lie brackets and $\cdot^{[p]}$-operators.

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BibTeX RIS

Tyler J. Evans, Alice Fialowski, Yong Yang. 2024-02-22. On the Cohomology of Restricted Heisenberg Lie Algebras. https://arxiv.org/abs/2402.14249

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