Homotopy Equivalences induced by Balanced Pairs

By Xiao-Wu Chen. 2008

83 citations recorded by the source corpus.

We introduce the notion of balanced pair of additive subcategories in an abelian category. We give sufficient conditions under which the balanced pair of subcategories gives rise to equivalent homotopy categories of complexes. As an application, we prove that for a left-Gorenstein ring, there exists a triangle-equivalence between the homotopy category of its Gorenstein projective modules and the homotopy category of its Gorenstein injective modules, which restricts to a triangle-equivalence between the homotopy category of projective modules and the homotopy category of injective modules. In the case of commutative Gorenstein rings we prove that up to a natural isomorphism our equivalence extends Iyengar-Krause's equivalence.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/67e223ad3a4412679134815831827efeccb0c42f

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In Algebra and Number Theory

1. Xiao-Wu Chen
2. Apostolos Beligiannis
3. P. Ara
4. Pu Zhang
5. Kulumani M. Rangaswamy

In Geometry and Topology

1. Xiao-Wu Chen
2. Apostolos Beligiannis
3. P. Ara
4. Pu Zhang
5. Kulumani M. Rangaswamy

In Mathematical Physics

1. Xiao-Wu Chen
2. Apostolos Beligiannis
3. P. Ara
4. Kulumani M. Rangaswamy

Citations in the corpus

• Gorenstein Homological Algebra of Artin Algebras (2017, background): “The following is initiated by Gao and Zhang [31]; also see [22].”