Year: 2026
Type: preprint
Abstract: 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, its associated graded algebra is the current algebra part of Garland's integral form. As applications, over an algebraically closed field of characteristic $p>3$, we identify the small Yangian with the restricted Yangian and classify their finite dimensional simple modules in terms of restricted Drinfeld polynomials.
Source: arXiv (Cornell University)
Authors: Chang, Hao, Hu, Hongmei, Hu, Yue
Institution: Central China Normal University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G5057393290, G5125679948, G9000377871
OpenAlex ID: W7220650079