Triangulated categories of periodic complexes and orbit categories

Liu, Jian

Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 765-792

Abstract (VO)

We investigate the triangulated hull of orbit categories of the perfect derived category and the bounded derived category of a ring concerning the power of the suspension functor. It turns out that the triangulated hull corresponds to the full subcategory of compact objects of certain triangulated categories of periodic complexes. This specializes to Stai and Zhao's result on the finite dimensional algebra of finite global dimension. As the first application, if $A$, $B$ are flat algebras over a commutative ring and they are derived equivalent, then the corresponding derived categories of $n$-periodic complexes are triangle equivalent. As the second application, we get the periodic version of the Koszul duality.

Détail

DOI : 10.21136/CMJ.2023.0234-22

Classification : 16E45, 18E20, 18G35, 18G80
Keywords: periodic complex; orbit category; triangulated hull; derived category; derived equivalence; dg category; Koszul duality

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