Degree 3 Cohomological Invariants of Split Simple Groups that are Neither Simply Connected nor Adjoint

Abstract

In a recent paper A. Merkurjev constructed an exact sequence which includes as one of the terms the group of degree 3 normalized cohomological invariants of a semisimple algebraic group G, greatly extending results of M. Rost for simply connected simple groups. Furthermore in the aformentioned paper Merkurjev uses his exact sequence to determine the groups of invariants for all semisimple adjoint groups of inner type. The goal of this paper is to use Merkurjevs exact sequence to compute the group of invariants for the remaining split cases, namely groups of types A and D that are neither simply connected nor adjoint, and to investigate the way that the invariants restrict to subgroups in some specific cases of interest.