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Mathematics > Representation Theory

arXiv:2208.03783 (math)
[Submitted on 7 Aug 2022]

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

Authors: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.
Comments: 20 pages, 9 page appendix
Subjects: Representation Theory (math.RT)
MSC classes: 17B50, 17B56, 17B67, 17B70
Cite as: arXiv:2208.03783 [math.RT]
  (or arXiv:2208.03783v1 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.2208.03783

Submission history

From: Tyler J. Evans [view email]
[v1] Sun, 7 Aug 2022 18:15:45 UTC (56 KB)
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