Cohomology for infinitesimal unipotent algebraic and quantum groups |
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Authors: | Christopher M Drupieski Daniel K Nakano Nham V Ngo |
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Institution: | 1. Department of Mathematics, University of Georgia, Athens, GA, 30602, USA
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Abstract: | In this paper we study the structure of cohomology spaces for the Frobenius kernels of unipotent and parabolic algebraic group schemes and of their quantum analogs. Given a simple algebraic group G, a parabolic subgroup P J , and its unipotent radical U J , we determine the ring structure of the cohomology ring H?((U J )1, k). We also obtain new results on computing H?((P J )1, L(??)) as an L J -module where L(??) is a simple G-module with highest weight ?? in the closure of the bottom p-alcove. Finally, we provide generalizations of all our results to small quantum groups at a root of unity. |
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