Cohomology of unipotent algebraic and finite groups and the Steenrod algebra (Q1329036)

Let \(G\) be an affine algebraic group over a finite field \(k\). It is shown that there is a homomorphism from the coordinate ring \(k[G]\) to the dual of the group ring \(k(G(k))\). It induces a cohomology map. When \(G\) is unipotent, this leads to a previous result of D. Radford. Next the author deals with a maximal unipotent subgroup \(U\) of \(\text{GL}_ m\) defined over \(\mathbb{F}_ 2\). The cohomology of \(\text{GL}_ n(k)\) with coefficients in \(k\) is studied. The Steenrod algebra is used.