Correspondence functors and finiteness conditions

JOURNAL OF ALGEBRA

卷:495

Article

Bouc, Serge¹  Thevenaz, Jacques² 

[1] Univ Picardie Jules Verne, CNRS LAMFA, 33 Rue St Len, F-80039 Amiens 1, France

[2] Ecole Polytech Fed Lausanne, Sect Math, Stn 8, CH-1015 Lausanne, Switzerland

关键词: Finite set;    Correspondence;    Functor category;    Simple functor;    Finite length;    Poset;   

DOI  :  10.1016/j.jalgebra.2017.11.010

来源: Elsevier

【 摘 要 】

We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various specific properties which do not hold for other types of functors. In particular, if k is a field and if F is a correspondence functor, then F is finitely generated if and only if the dimension of F(X) grows exponentially in terms of the cardinality of the finite set X. Moreover, in such a case, F has actually finite length. Also, if k is noetherian, then any subfunctor of a finitely generated functor is finitely generated. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free