Representations of Lie algebras in prime characteristic
Representations of Lie algebras in prime characteristic
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DOI：
10.1007/978-94-015-9131-7_5
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
J. Jantzen
中科院分区：
文献类型：
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作者：
J. Jantzen
这些讲座的目的是对具有素数特征的约化群的李代数的表示理论进行综述。这个理论在特征O上与相应的理论有很大的不同。例如，在素特征上，所有的单模都是有限维的。另一方面，在大多数情况下，没有对这些简单模块进行分类。在过去的几年里，这方面已经取得了很大的进展，主要是关于Premet(1995)对Kac-Weisfeeller猜想(1971)的证明。前四节讨论了一般(限制)李代数的素特征表示理论，以及在幂等可解李代数的情况下的一些特殊方面。然后，文本的其余部分更具体地处理还原群的李代数。
The aim of these lectures is to give a survey on the representation theory of Lie algebras of reductive groups in prime characteristic. This theory is quite different from the corresponding theory in characteristic O. For example, in prime characteristic all simple modules are finite dimensional. On the other hand, there is in most cases no classification of these simple modules. There has been major progress in this area in the last few years, mostly related to Premet’s proof (from 1995) of the Kac-Weisfeiler conjecture (from 1971).The first four sections discuss the representation theory of general (restricted) Lie algebras in prime characteristic as well as some special aspects in the cases of unipotent and solvable Lie algebras. The rest of the text then deals more specifically with Lie algebras of reductive groups.