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arXiv · 2208.03783

Central Extensions of Restricted Affine Nilpotent Lie Algebras $n_+(A^{(1)}_1)(p)$

Tyler J. Evans·Alice Fialowski
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Abstract

Consider the maximal nilpotent subalgebra $n_+(A_1^{(1)})$ of the simplest affine algebra $A_1^{(1)}$ which is one of the $\mathbb{N}$-graded Lie algebras with minimal number of generators. We show truncated versions of this algebra in positive characteristic admit the structure of a family of restricted Lie algebras. We compute the ordinary and restricted 1- and 2-cohomology spaces with trivial coefficients by giving bases. With these we explicitly describe the restricted 1-dimensional central extensions.

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BibTeXRIS

Tyler J. Evans, Alice Fialowski. 2022-08-07. Central Extensions of Restricted Affine Nilpotent Lie Algebras $n_+(A^{(1)}_1)(p)$. https://arxiv.org/abs/2208.03783

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