发表机构
Central China Normal University; Shanghai Maritime University; Beijing University of Posts and Telecommunications（华中师范大学; 上海海事大学; 北京邮电大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为经典类型Yangian构造了由Drinfeld生成元分次幂生成的Z[1/2]-积分形式，建立三角分解与PBW基，并在特征p>3时将其模p约化与受限Yangian等同。
AI 中文摘要
设$\mathfrak g$为经典类型的单李代数。我们构造了由正、负Drinfeld生成元的分次幂生成的Yangian $Y(\mathfrak g)$的一个$\mathbb Z[1/2]$-积分形式，并建立了其三角分解和PBW基。在环过滤下，我们积分形式的相伴分次代数是Garland积分形式的当前代数部分。作为应用，在特征$p>3$的代数闭域上，我们将模$p$约化得到的小Yangian与受限Yangian等同起来。
英文摘要
Let $\mathfrak g$ be a simple Lie algebra of classical type. We construct a $\mathbb Z[1/2]$-integral form of the Yangian $Y(\mathfrak g)$ generated by divided powers of the positive and negative Drinfeld generators, and establish its triangular decomposition and PBW basis. Under the loop filtration, the associated graded algebra of our integral form is the current algebra part of Garland's integral form. As an application, over an algebraically closed field of characteristic $p>3$, we identify the small Yangian obtained by reduction modulo $p$ with the restricted Yangian.
Comments28 pages, comments welcome!
