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In Chapter 2, starting from a generalization of Hensel's Lemma to non-commutative case, we introduce the Brauer characters and the generalized decomposition numbers, and construct a kind of maximal semisimple algebras; then, similarly to Puig's methods, we prove Brauer's Second Main Theorem over arbitrary fields; applying it to blocks with nilpotent coefficient extensions, a formula on characters of such blocks is given; the formula of characters of nilpotent blocks is just an easy consequence of the fomula.

在第二章中,我们将Hensel的引理推广到非交换的情况,以此为起点,定义了Brauer特征标和广义分解数,构造了一类极大的半单的代数,类似于Puig的方法,给出了任意域上Brauer的第二主要定理;作为该定理的应用,我们给出了具有幂零系数扩张的块的特征标公式,幂零块的特征标公式只是它的一个简单的推论。

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