有限半群的本原表示I
Primitive representations of finite semigroups I
摘要：
有限群的本原表示和本原有限群在O 'Nan-Scott定理中得到了分类。本文对忠实有限本原半群表示进行了分类。对于每个有限本原表示，我们将一个不变式，一个有限维矩阵与一个本原有限群表示中的元素相关联。在很大程度上，这个矩阵决定了代表性。在本系列的后续论文中，将进一步探讨不变量。我们的可导性结果依赖于两个主要思想，其中之一是R. McKenzie，而另一个是我们的Rees矩阵理论的适应有限半群的表示论。利用后一种思想，我们能够提供有限半群的正则T类的所有表示的描述。
英文摘要：
Primitive representations of finite groups as well as primitive finite groups were classified in the O'Nan-Scott Theorem. In this paper we classify faithful finite primitive semigroup representations. To each finite primitive representation, we associate an invariant, a finite dimensional matirix with entries in a primitive finite groups representation. To a large extent, this matrix determines the representation. In later papers in this series the invariant is further explored. Our primitivity resoullts rely on two main ideas, one of which is a small but important part of the theory of tame algebras developed by R. McKenzie, while the other is our adaptation of Rees matrix theory to the representation theory of finite semigroups. Using the latter idea we are able to provide a description of all representations of a regular T class of a finite semigroup.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
