Characters of finite semigroups
Characters of finite semigroups
复制标题
有限半群的性质
DOI：
10.1016/0021-8693(72)90111-1
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发表时间：
1972
影响因子：
0.9
通讯作者：
D. Mcalister
中科院分区：
文献类型：
--
作者：
D. Mcalister
设S是有限半群，J1，…，Jr是S的正则j-类.本文的主要定理是：chS ∈ chH 1X···XchHr其中，chS表示S的特征环，H1，.，Hr分别是J1，..，Jr的极大子群.作为这个结果的结果，S的两个表示等价当且仅当它们在S的子群上等价。此外，我们表明，每个字符的S可以唯一地表示为一个完整的线性组合，我们称之为标准的不可约字符。因此，Brauer [1]的一个重要定理的类似定理对有限半群也成立;即，有限半群的每个特征标都可以表示为由其基本子群的线性特征标导出的特征标的整数线性组合。
Let S be a finite semigroup and let J 1,…, J r be the regular j-classes of S. Then the main theorem of this paper shows that ch S≈ ch H 1 X··· X ch H r where, for example, ch S denotes the character ring of S and H 1,…, H r are maximal subgroups of J 1,…, J r, respectively. As a consequence of this result, two representations of S are equivalent if and only if they are equivalent on the subgroups of S. Further, we show that each character of S can be uniquely expressed as an integral linear combination of what we term standard irreducible characters. As a consequence of this, the analog of an important theorem of Brauer [1] holds for finite semigroups; namely, every character of a finite semigroup can be expressed as an integral linear combination of characters induced from linear characters of its elementary subgroups.