射影Brauer(模表示)理论的第一主定理(英文)  

The First Main Theorem of Projective Brauer Theory

作　　者：沈明辉[1] 

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南大学学报（自然科学版）》2008年第4期1-6,共6页Journal of Southwest University(Natural Science Edition)

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).This paper is a report on a part of the author＇s research on projective Brauer characters. Based on the notions 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 correspondence 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 invariants, the so-called defect classes and defect groups, for such a-blocks. Then the autho：r proves a projective version of the first main theorem for such a-blocks by character-theoretic method, which contains the classical Brauer＇s first main theorem as a special case （i. e. when a = 1）. The details of the proofs are omitted here due to the limitation of space.

关 键 词：Brauer同态 亏类 亏群 Brauer对应 a-块 

分 类 号：O152.6[理学—数学]