射影Brauer(模表示)理论的第一主定理
The First Main Theorem of Projective Brauer Theory
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摘要: 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α-块引入了所谓亏类和亏群的不变量,并建立了群G的某类α-块和群G的局部子群的此类α-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α=1时).Abstract: 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.
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