On nilpotent commuting varieties and cohomology of Frobenius kernels

2014/01/27 by Nham V. Ngo, Ngo, Nham V. · 1 citation
Mathematics · #13A50 #13C14 #20Gxx #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT) #math.AC #math.RT #msc:13A50 #msc:13C14 #msc:20Gxx

paper · pdf · doi:10.48550/arxiv.1401.6820

To appear in the Journal of Algebra (2015)

arxiv created 2014/12/16 · arxiv updated 2014/12/17

Abstract

The paper studies the dimensions of irreducible components of commuting varieties of (restricted) nilpotent r-tuples in a classical Lie algebra \mathfrakg defined over an algebraically closed field k. As applications, we obtain some new results on the structure of the (even) cohomology ring of Frobenius kernels G_r for each r≥ 1, where G is the simply connected, simple algebraic group such that Lie(G)=\mathfrakg. Explicit calculations for rank two groups are also presented.

Cited by

• Invariants for \mathbb G_(r)-modules

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