Representations and cohomology for Frobenius-Lusztig kernels

Details Representations and cohomology for Frobenius-Lusztig kernels Representations and cohomology for Frobenius-Lusztig kernels

2010-04-25

arxiv.org/abs/1004.4315v2

J. Pure Appl. Algebra 215 (2011), no. 6, 1473-1491

Mathematics

Representation Theory

26 pages. Incorrect references fixed

Scientific paper

10.1016/j.jpaa.2010.09.006

Let $U_\zeta$ be the quantum group (Lusztig form) associated to the simple Lie algebra $\mathfrak{g}$, with parameter $\zeta$ specialized to an $\ell$-th root of unity in a field of characteristic $p>0$. In this paper we study certain finite-dimensional normal Hopf subalgebras $U_\zeta(G_r)$ of $U_\zeta$, called Frobenius-Lusztig kernels, which generalize the Frobenius kernels $G_r$ of an algebraic group $G$. When $r=0$, the algebras studied here reduce to the small quantum group introduced by Lusztig. We classify the irreducible $U_\zeta(G_r)$-modules and discuss their characters. We then study the cohomology rings for the Frobenius-Lusztig kernels and for certain nilpotent and Borel subalgebras corresponding to unipotent and Borel subgroups of $G$. We prove that the cohomology ring for the first Frobenius-Lusztig kernel is finitely-generated when $\g$ has type $A$ or $D$, and that the cohomology rings for the nilpotent and Borel subalgebras are finitely-generated in general.

Affiliated with

Also associated with

No associations

Rating

Representations and cohomology for Frobenius-Lusztig kernels 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 Representations and cohomology for Frobenius-Lusztig kernels, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representations and cohomology for Frobenius-Lusztig kernels will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-186202