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 $\mathfrak{gl}_3(k)$.