1997/11/22 by Steve Seif, Seif, Steve, Johnny Ray Sena +1
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings and Algebras (math.RA) #math.RA #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/9711226
arxiv created 1997/11/22 · openalex publication_date 1997/11/22 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.