Super Yangians in characteristic $2$

TL;DR

This paper introduces super Yangians over fields of characteristic 2, showing they deform the super universal enveloping algebra of current Lie algebras and describing their centers.

Contribution

It defines super Yangians in characteristic 2 and characterizes their structure and center, extending previous work to a new algebraic setting.

Findings

Super Yangians are deformations of super universal enveloping algebras.

The structure of the center of super Yangians is described.

The methods extend known techniques to characteristic 2 fields.

Abstract

We define the super Yangian $Y_{m|n}$ over a field $\mathbbm{k}$ of characteristic $2$, and show that the super Yangian $Y_{m|n}$ is a deformation of the super universal enveloping algebra of the current Lie algebra $\mathfrak{gl}_{m+n}[t]$. By employing the methods of the work of \cite{BT18}, we also give a description of the center of $Y_{m|n}$.