论文标题
限制仿射nilpotent lie代数$ n _+（a^{（1）} _ 1）（p）$的中心扩展
Central Extensions of Restricted Affine Nilpotent Lie Algebras $n_+(A^{(1)}_1)(p)$
论文作者
论文摘要
考虑最简单的仿射代数$ a_1^{（1）} $的最大nilpotent subalgebra $ n _+（a_1^{（1）}）$，这是$ \ m athbb {n} $ - 分级的lie代数之一。我们在积极特征中显示了该代数的截短版本，承认有限的谎言代数家族的结构。我们通过给出碱基来计算具有微不足道系数的普通和受限制的1-和2-循环空间。通过这些，我们明确描述了受限制的一维中心扩展。
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.
