Irreducible matrix representations of finite semigroups
Irreducible matrix representations of finite semigroups
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有限半群的不可约矩阵表示
DOI：
10.1090/s0002-9947-1969-0242973-3
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发表时间：
1969
影响因子：
1.3
通讯作者：
M. Petrich
中科院分区：
文献类型：
--
作者：
G. Lallement;M. Petrich
Munn [9]证明了对于满足主理想极小条件的半群S，S的不可约表示与其0-单（或单）主因子在零处为零的不可约表示之间存在自然的一一对应;对于S有限的情况，参见Ponizovskii [1 1]。另一方面，Clifford [3]和[4]得到了完全0-单半群的所有表示作为其极大子群的表示的“扩张”。结合他们的结果，原则上可以得到满足关于主左理想和主右理想的极小条件的半群的所有不可约表示，从而得到有限半群的所有不可约表示。然而，在构造完全0-单半群S=，，&'（G; I，A; P）的表示时，必须解决矩阵论中的分块矩阵的分解问题
Munn [9] has shown that for a semigroup S satisfying the minimal condition on principal ideals, there is a natural one-to-one correspondence between irreducible representations of S and irreducible representations vanishing at zero of its 0-simple (or simple) principal factors; for the case of S finite, see Ponizovskii [1 1]. On the other hand, Clifford, [3] and [4], has obtained all representations of a completely 0-simple semigroup as "extensions" of those of its maximal subgroups. Combining their results, one can, in principle, obtain all irreducible representations of a semigroup satisfying the minimal conditions on principal left and right ideals and thus of finite semigroups. However, in constructing the representations of a completely 0-simple semigroup S=,,&'(G; I, A; P), one has to solve the problem in matrix theory of factoring the block matrix