Journal of Lie Theory

no. 1
Central Extensions of Restricted Affine Nilpotent Lie Algebras n+(A1(1))(p)
Journal of Lie Theory, Volume 33 (2023) no. 1, pp. 195-215
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 2-cohomology spaces with trivial coefficients by giving bases. With these we explicitly describe the restricted 1-dimensional central extensions.
DOI: 10.5802/jolt.1280
Classification: 17B50, 17B56,17B67, 17B70
Keywords: Restricted Lie algebra, cohomology, central extension, affine Lie algebra 
@article{JOLT_2023_33_1_a8,
     author = {T. J. Evans and A. Fialowski},
     title = {Central {Extensions} of {Restricted} {Affine} {Nilpotent} {Lie} {Algebras} {n\protect\textsubscript{+}(A\protect\textsubscript{1}\protect\textsuperscript{(1)})(p)}},
     journal = {Journal of Lie Theory},
     pages = {195--215},
     year = {2023},
     volume = {33},
     number = {1},
     doi = {10.5802/jolt.1280},
     zbl = {1555.17021},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1280/}
}
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T. J. Evans; A. Fialowski. Central Extensions of Restricted Affine Nilpotent Lie Algebras n+(A1(1))(p). Journal of Lie Theory, Volume 33 (2023) no. 1, pp. 195-215. doi: 10.5802/jolt.1280

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