Toggle Main Menu Toggle Search

Open Access padlockePrints

Symmetric Auslander and Bass categories

Lookup NU author(s): Professor Peter Jorgensen

Downloads


Abstract

We define the symmetric Auslander category A(s) (R) to consist of complexes of projective modules whose left- and right-tails are equal to the left- and right-tails of totally acyclic complexes of projective modules. The symmetric Auslander category contains A(R), the ordinary Auslander category. It is well known that A(R) is intimately related to Gorenstein projective modules, and our main result is that A(s) (R) is similarly related to what can reasonably be called Gorenstein projective homomorphisms. Namely, there is an equivalence of triangulated categories (GMor) under bar (R) ->(similar or equal to) A(s)(R)/K-b(Prj R) where (GMor) under bar (R) is the stable category of Gorenstein projective objects in the abelian category Mor(R) of homomorphisms of R-modules. This result is set in the wider context of a theory for A(s) (R) and B-s (R), the symmetric Bass category which is defined dually.


Publication metadata

Author(s): Jorgensen P, Kato K

Publication type: Article

Publication status: Published

Journal: Mathematical Proceedings of the Cambridge Philosophical Society

Year: 2011

Volume: 150

Pages: 227-240

Print publication date: 01/03/2011

Date deposited: 16/10/2012

ISSN (print): 0305-0041

ISSN (electronic): 1469-8064

Publisher: Cambridge University Press

URL: http://dx.doi.org/10.1017/S0305004110000629

DOI: 10.1017/S0305004110000629


Altmetrics

Altmetrics provided by Altmetric


Funding

Funder referenceFunder name
18540044JSPS

Share