Source Algebras and Source Modules
Source Algebras and Source Modules
复制标题
源代数和源模块
DOI：
10.1006/jabr.2000.8625
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发表时间：
2001
影响因子：
0.9
通讯作者：
R. Rouquier
中科院分区：
文献类型：
--
作者：
J. Alperin;M. Linckelmann;R. Rouquier
本文的目的是根据 Puig 6, 14.6 为块理论中的两个基本结果提供模理论术语中的自包含方法：首先，将某个有限群的块的布劳尔对应项的源代数嵌入到该块的源代数中，其次，可以明确地描述布劳尔对应项的源代数。我们对第一个结果定理 5 及其推论 6 的证明本质上是对 1, 4.10 中证明的术语的翻译。第二个结果描述了布劳尔通讯员的源代数，也来自 3，但 3 中的证明既使用了 5 中幂零块结构的主要结果，也使用了 6 中的技术。 4, 6，而我们从命题 9 开始的方法只需要一些关于具有中心缺陷组的块结构的经典结果。对具有正常缺陷群的块的源代数的结果的说明也可以在第 7 节中找到。 45，除了 ^ Ž 。中心扩展 E 的显式描述参见下面第 10 节，它是根据块的重数代数定义的，即 Ž .Ž 。 7, 45.10 b 中引用，没有证据，参考 7, 节末尾的 6。 45.
The aim of this article is to give a self-contained approach in module theoretic terms to two fundamental results in block theory, due to Puig 6, 14.6 : first, there is an embedding of the source algebra of the Brauer correspondent of a block of some finite group into a source algebra of that block, and second, the source algebras of the Brauer correspondence can be described explicitly. Our proof of the first result Theorem 5 and its Corollary 6 below is essentially the translation to our terminology of the proof in 1, 4.10 . The second result, describing the source algebras of the Brauer correspondent, follows also from 3 , but the proofs in 3 use both the main result on the structure of nilpotent blocks in 5 as well as techniques from 6, Sects. 4, 6 , while our approach from Proposition 9 onwards requires only some classical results on the structure of blocks with a central defect group. An account of the results in 6 on source algebras of blocks with a normal defect group can also be found in 7, Sect. 45 , except for the ˆ Ž . explicit description of the central extension E see Section 10 below , as being defined in terms of the multiplicity algebra of the block, which is Ž .Ž . quoted in 7, 45.10 b without proof, referring back to 6 at the end of 7, Sect. 45 .