Monomorphism categories, cotilting theory, and Gorenstein-projective modules

JOURNAL OF ALGEBRA

卷:339

Article

Zhang, Pu

关键词: Monomorphism category;    Cotilting modules;    Gorenstein-projective modules;   

DOI  :  10.1016/j.jalgebra.2011.05.018

来源: Elsevier

【 摘 要 】

The monomorphism category S(n)(X) is introduced, where X is a full subcategory of the module category A-mod of an Artin algebra A. The key result is a reciprocity of the monomorphism operator S(n), and the left perpendicular operator (perpendicular to): for a cotilting A-module T. there is a canonical construction of a cotilting module m(T) over the upper triangular matrix algebra T,,(A), such that S(n)((perpendicular to)T)= (perpendicular to)m(T). As applications, S(n)(X) is a resolving contravariantly finite subcategory in T(n)(A)-mod with <(S(n)(X))over cap> = T(n)(A)-mod if and only if X is a resolving contravariantly finite subcategory in A-mod with (X) over cap = A-mod. For a Gorenstein algebra A. the category T(n)(A)-gproj of Gorenstein-projective T(n)(A)-modules can be explicitly determined as S(n)((perpendicular to)A). Also, self-injective algebras A can be characterized by. the property T(n)(A)-gproj = S(n)(A). Finally, we obtain a characterization of those categories S(n)(A) which have finite representation type in terms of Auslander's representation dimension. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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