Degree three invariants for semisimple groups of types $B$, $C$, and $D$

Abstract

We determine the group of reductive cohomological degree $3$ invariants of all split semisimple groups of types $B$, $C$, and $D$. We also present a complete description of the cohomological invariants. As an application, we show that the group of degree $3$ unramified cohomology of the classifying space $BG$ is trivial for all split semisimple groups $G$ of types $B$, $C$, and $D$.

Proof of Proposition 6.13 revised; Lemma 6.14 removed

References in corpus (2)

• The rationality problem for fields of invariants under linear algebraic groups (with special regards to the Brauer group)
• Degree 3 Cohomological Invariants of Groups that are Neither Simply Connected nor Adjoint