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Lookup NU author(s): Professor Peter Jorgensen
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.
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
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