Character theory of monoids over an arbitrary field

JOURNAL OF ALGEBRA

卷:431

Article

Masuda, Ariane M.¹  Quoos, Luciane²  Steinberg, Benjamin³ 

[1] New York City Coll Technol, Dept Math, Brooklyn, NY 11201 USA

[2] Univ Fed Rio de Janeiro, Inst Matemat, BR-21941909 Rio De Janeiro, RJ, Brazil

[3] CUNY City Coll, Dept Math, New York, NY 10031 USA

关键词: Character theory;    Representation theory;    Monoids;   

DOI  :  10.1016/j.jalgebra.2015.02.017

来源: Elsevier

【 摘 要 】

The basic character theory of finite monoids over the complex numbers was developed in the sixties and seventies based on work of Munn, Ponizovskii, McAlister, Rhodes and Zalcstein. In particular, McAlister determined the space of functions spanned by the irreducible characters of a finite monoid over C and the ring of virtual characters. In this paper, we present the corresponding results over an arbitrary field. As a consequence, we obtain a quick proof of the theorem of Berstel and Fteutenauer that the characteristic function of a regular cyclic language is a virtual character of the free monoid. This is a crucial ingredient in their proof of the rationality of the zeta function of a sofic shift in symbolic dynamics. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free