Torsion in cohomology of compact Lie groups and Chow rings of reductive algebraic groups (Q1059312)

The author gives an explicit description of the cohomology ring \(H^*(K,{\mathbb{F}}_ p)\) with coefficients in an arbitrary finite field \({\mathbb{F}}_ p\) of any connected compact Lie group K if \(p>2\), or of any simply connected compact K if \(p=2\); the description is given also for the Chow ring \(A(G,{\mathbb{F}}_ p)\) of the corresponding complex algebraic group G. The description is given in terms of the set of degrees of basic W-invariants over \({\mathbb{Q}}\) of the corresponding root system and its subset of ''p-exceptional degrees''. Since these ''p-exceptional degrees'' can be calculated from the degrees of the basic ''generalized W- invariants'' the procedure reduces to a purely ''Weyl group'' question.