Recollement of Homotopy Categories and Cohen-Macaulay Modules (Representation Theory of Finite Groups and Algebras, and Related Topics)
By Osamu Iyama, Kiriko Kato, Jun-ichi Miyachi. 2009
51 citations recorded by the source corpus.
We study the homotopy category of unbounded complexes with bounded homologies and its quotient category by the homotopy category of bounded complexes. We show the existence of a recollement of the above quotient category and it has the homotopy category of acyclic complxes as a triangulated subcategory. In the case of the homotopy category of finitely generated projective modules over an Iwanaga-Gorenstein ring, we show that the above quotient category are triangle equivalent to the stable module category of Cohen-Macaulay $\opn{T}_2(R)$-modules.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/dca849c7dcfd796225a8ed75fbf4514a09a2641a
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Monic representations and Gorenstein-projective modules (2011, background): “This class of modules enjoys more stable properties than the usual projective modules (see [Auslander and Bridger 1969], where it was called a module of G-dimension zero); it becomes a main ingredient in the relative homological algebra [Enochs and Jenda 1995; 2000] and in the representation theory ”
- On singular equivalences of Morita type (2013, unknown): “We mention in particular Xiao-Wu Chen’s work here [6–9], but also Bernhard Keller, Daniel Murfet and Michel van den Bergh [15] as well as Osamu Iyama, Kiriko Kato and Jun-Ichi Miyachi [13].”