Degree 3 Cohomological Invariants of 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 quasi-simple groups. Furthermore, in the aforementioned 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 Merkurjev's 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. This description not only demonstrates the existence of many previously unstudied invariants but also allows us to extend several known results which relate these invariants to the Rost invariant and algebras with involution.