Cohomology of ${\mathfrak{sl}}_3$ and ${\mathfrak{gl}}_3$ with Coefficients in Simple Modules and Weyl Modules in Positive Characteristics

Abstract

We calculate the cohomology of ${\mathfrak{sl}}_3(k)$ over an algebraically closed field $k$ of characteristic $p>3$ with coefficients in simple modules and Weyl modules. We also give descriptions of the corresponding cohomology of ${\mathfrak{gl}}_3(k)$.