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Super Yangians in characteristic $2$

Hao Chang, Hongmei Hu

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 $Y_{m|n}$.

Super Yangians in characteristic $2$

Abstract

We define the super Yangian over a field of characteristic , and show that the super Yangian is a deformation of the super universal enveloping algebra of the current Lie algebra . By employing the methods of the work of \cite{BT18}, we also give a description of the center of .
Paper Structure (9 sections, 10 theorems, 65 equations)

This paper contains 9 sections, 10 theorems, 65 equations.

Table of Contents

  1. Introduction
  2. Lie superalgebras
  3. The current Lie algebra
  4. Lie superalgebras in characteristic $2$
  5. The center of $U_{\mathop{\mathrm{super}}\nolimits}(\mathfrak{g})$
  6. Super Yangian in characteristic $2$
  7. Modular Yangian $Y_{m+n}$
  8. Super Yangians in characteristic $2$
  9. The center of $Y_{m|n}$

Key Result

Proposition 2.1

The enveloping algebra $U(\mathfrak{g})$ is free as a module over $Z_{p,\mathop{\mathrm{odd}}\nolimits}(\mathfrak{g})$ with basis given by the ordered supermonomials in the following elements of $\mathfrak{g}$ In particular, the above ordered supermonomials forms a linear basis for $U_{\mathop{\mathrm{super}}\nolimits}(\mathfrak{g})$.

Theorems & Definitions (19)

  • Definition
  • Proposition 2.1
  • Lemma 2.2
  • proof
  • Theorem 2.3
  • proof
  • Theorem 3.1
  • Theorem 3.2
  • Remark 3.3
  • Theorem 3.4
  • ...and 9 more