Cohomology of classical algebraic groups from the functorial viewpoint

Details Cohomology of classical algebraic groups from the functorial viewpoint Cohomology of classical algebraic groups from the functorial viewpoint

2009-02-25

arxiv.org/abs/0902.4459v3

Adv. Math. 225 (2010), no. 1, 33-68

Mathematics

Representation Theory

41 pages. v3. minor changes: misprints corrected, references added, sections 3.1 step 2, and 3.3 step 2 expanded

Scientific paper

We prove that extension groups in strict polynomial functor categories compute the rational cohomology of classical algebraic groups. This result was previously known only for general linear groups. We give several applications to the study of classical algebraic groups, such as a cohomological stabilization property, the injectivity of external cup products, and the existence of Hopf algebra structures on the (stable) cohomology of a classical algebraic group with coefficients in a Hopf algebra. Our result also opens the way to new explicit cohomology computations. We give an example inspired by recent computations of Djament and Vespa.

Affiliated with

Also associated with

No associations

Rating

Cohomology of classical algebraic groups from the functorial viewpoint does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cohomology of classical algebraic groups from the functorial viewpoint, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cohomology of classical algebraic groups from the functorial viewpoint will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-253646