Cohomology of infinitesimal algebraic groups (Q750624)

Let B be a Borel subgroup in a reductive algebraic group over an algebraically closed field k of positive characteristic p, and let \(B_ r\) denote the r'th Frobenius kernel in B. This paper deals with computations of the Hochschild cohomology groups \(H^ i(B_ r,k)\). For \(r=1\) (and p large), these groups were determined by \textit{J. C. Jantzen} and the reviewer [Math. Ann. 269, 487-525 (1984; Zbl 0529.20027)] while already \(r=2\) presents a very hard problem even for small groups. In the paper under review, the authors obtain results in low degree for general r when the group is SL\({}_ n\) and for the group SL\({}_ 3\) they have detailed computations in all degrees for the case \(r=2\).