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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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