Integral forms for Yangians of classical type

Let $\mathfrak{g}$ be a simple Lie algebra of classical type. We construct a $\mathbb{Z}[1\mathrm{/}2]$-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.