Explicit HRS-Tilting

Details Explicit HRS-Tilting Explicit HRS-Tilting

2007-04-08

arxiv.org/abs/0704.1008v2

Mathematics

Representation Theory

31 pages, introduction expanded, minor errors corrected

Scientific paper

For an abelian category $A$ equipped with a torsion pair, we give an explicit description for the abelian category $B$ introduced by Happel-Reiten-Smalo, and also for the category of chain complexes $Ch(B)$ and the derived category $D(B)$ of $B$. We also describe the DG structure on $Ch(B)$. As a consequence, we find new proofs of certain results of Happel-Reiten-Smalo. The main ingredient is the category of {\em decorated} complexes.

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