On the second cohomology of an algebraic group and of its Lie algebra in a positive characteristic (Q2401648)

Let \(G\) be an algebraic group over an algebraically closed field of positive characteristic \(p\) and \(\mathfrak g\) its Lie group. Suppose that \(p\geqslant 3h-3\) where \(h\) is the Coxeter number. The main result of the paper is a criteria under which the second cohomology group of \(G\) and of \(\mathfrak g\) with coefficients in a simple module are isomorphic. Similar result for the first cohomology group was obtained by the author in the paper [Math. Notes 96, No. 4, 491--498 (2014; Zbl 1339.20039); translation from Mat. Zametki 96, No. 4, 512--521 (2014)].