Journal of the Ramanujan Mathematical Society
Volume 29, Issue 4, December 2014 pp. 465–481.
Degree 3 cohomological invariants of split simple groups that are neither simply connected nor adjoint
Authors:
Hernando Bermudez and Anthony Ruozzi
Author institution:Department of Mathematics & Computer Science, Emory University, Atlanta, GA 30322, USA
Summary:
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 Merkurjev's 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.
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