Cohomology for Frobenius kernels of SL2

[摘要] Let (SL2)(r) be the r-th Frobenius kernels of the group scheme SL2 defined over an algebraically closed field of characteristic p > 0. In this paper we give for r >= 1 a complete description of the cohomology groups for (SL2)(r). We also prove that the reduced cohomology ring H-center dot ((SL2)(r), k)(red) is Cohen-Macaulay. Geometrically, we show for each r >= 1 that the maximal ideal spectrum of the cohomology ring for (SL2)(r) is homeomorphic to the fiber product G x (B) u(r). Finally, we adapt our calculations to obtain analogous results for the cohomology of higher Frobenius-Lusztig kernels of quantized enveloping algebras of type SL2. (C) 2013 Elsevier Inc. All rights reserved.

[发布日期] 2013-12-15

[关键词] Cohomology;Algebraic groups;Quantum groups;Frobenius kernels;Cohen-Macaulay