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Triangulated categories of periodic complexes and orbit categories. (English) Zbl 07729537

Summary: 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.

MSC:

18G80 Derived categories, triangulated categories
16E45 Differential graded algebras and applications (associative algebraic aspects)
18E20 Categorical embedding theorems
18G35 Chain complexes (category-theoretic aspects), dg categories
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