The characters of the symmetric inverse semigroup
The characters of the symmetric inverse semigroup
复制标题
DOI：
10.1017/s0305004100031947
复制
发表时间：
1957-01
影响因子：
0.8
通讯作者：
W. Munn
中科院分区：
文献类型：
--
作者：
W. Munn
在半群理论中，n个符号上的对称群有两个自然的类比，即n个符号的集合到其自身的所有映射的集合和这样一个集合的所有部分变换的集合，它们具有明显的乘法定义。我们在这里关注的是后一种系统。这是一个逆半群，因此我们称之为‘对称逆半群’。它产生特征为零的域或大于n的素数的域上的半单代数，因此它在这样的域上的矩阵表示是完全可约的。
There are two natural analogues of the symmetric group on n symbols in the theory of semigroups, namely, the set of all mappings of a set of n symbols into itself, and the set of all partial transformations of such a set, with the obvious definitions of multiplication. We are concerned here with the latter system. This is an inverse semigroup, and accordingly we call it the ‘symmetric inverse semigroup’. It gives rise to a semisimple algebra over a field of characteristic zero or a prime greater than n, and its matrix representations over such a field are thus completely reducible.