
Journal of Lie Theory 33 (2023), No. 1, 195215 Copyright Heldermann Verlag 2023 Central Extensions of Restricted Affine Nilpotent Lie Algebras n_{+}(A_{1}^{(1)})(p) Tyler J. Evans Department of Mathematics, California State Polytechnic University  Humboldt, Arcata, U.S.A. evans@humboldt.edu Alice Fialowski Faculty of Informatics, Eötvös Loránd University, Budapest, Hungary fialowski@inf.elte.hu [Abstractpdf] 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 that 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 2cohomology spaces with trivial coefficients by giving bases. With these we explicitly describe the restricted 1dimensional central extensions. Keywords: Restricted Lie algebra, cohomology, central extension, affine Lie algebra. MSC: 17B50, 17B56,17B67, 17B70. [ Fulltextpdf (170 KB)] for subscribers only. 