On the $1$-cohomology of $\mathrm{SL}(n,\mathbb{K})$ on the dual of its adjoint module

Ilaria Cardinali, Luca Giuzzi, Antonio Pasini

Given a field $\mathbb{K}$, for any $n\ge 3$ the first cohomology group $H^1(G_n,A_n^{\ast })$ of the special linear group $G_n=\mathrm{SL}(n,\mathbb{K})$ over the dual $A_n^{\ast }$ of its…