Homotopy Equivalences induced by Balanced Pairs

Details Homotopy Equivalences induced by Balanced Pairs Homotopy Equivalences induced by Balanced Pairs

2008-11-30

arxiv.org/abs/0812.0140v2

Journal of Algebra, 324 (2010), 2718-2731

Mathematics

Rings and Algebras

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Scientific paper

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.

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