Gorensteinness, homological invariants and Gorenstein derived categories

2014/01/16 by Gao, Nan
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1401.4202

Abstract

Relations between Gorenstein derived categories, Gorenstein defect categories and Gorenstein stable categories are established. Using these, the Gorensteinness of an algebra A and invariants with respect to recollements of the bounded Gorenstein derived category D^b_gp(A-\rm mod) of A are investigated. Specifically, the Gorensteinness of A is characterized in three ways: the existence of Auslander-Reiten triangles in D^b_gp(A-\rm mod); recollements of D^b_gp(A-\rm mod); and also Gorenstein derived equivalences. It is shown that the finiteness of Cohen-Macaulay type and of finitistic dimension are invariant with respect to the recollements of D^b_gp(A-\rm mod).

Related

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• Invariants and Gorenstein projective modules
• Gorenstein Homological Algebra of Artin Algebras
• On homotopy categories of Gorenstein modules: compact generation and dimensions
• Stability of Gorenstein objects in triangulated categories