射影Brauer(模表示)理论的第一主定理

对具有有限阶标准上循环的挠群代数定义了Brauer同态映射。利用这一概念，对群G的a-块引入了所谓亏类和亏群的不变量，并建立了群G的某类a-块和群G的局部子群的此类a-块之间的一一对应．然后根据已有结果，用特征标的方法证明了Brauer第一主定理的射影形式。这一定理包含了经典Brauer第一主定理为其特例（即当a=1时）。

The First Main Theorem of Projective Brauer Theory

This paper is a report on a part of the author's research on projective Brauer characters.Based on the no-tions and results obtained in the author's thesis,the author defines a Brauer homomorphism for certain twisted group algebras with standard cocycles of finite order.Using this notion,the author is able to establish a 1-1 corre-spondence between certain a-blocks of G with those of certain local subgroups of G.This is the content of Brauer's first main theorem for such projective characters and projective blocks.First,one also needs to introduce some in-variants,the so-called defect classes and defect groups,for such a-blocks.Then the author proves a projective ver-sion of the first main theorem for such a-blocks by character-theoretic method,which contains the classical Brauer'sfirst main theorem as a special case (i.e.when a=1).The details of the proofs are omitted here due to the limita-tion of space.