Triangulated categories of periodic complexes and orbit categories

Jian Liu

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 3, page 765-792
  • ISSN: 0011-4642

Abstract

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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 , are flat algebras over a commutative ring and they are derived equivalent, then the corresponding derived categories of -periodic complexes are triangle equivalent. As the second application, we get the periodic version of the Koszul duality.

How to cite

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Liu, Jian. "Triangulated categories of periodic complexes and orbit categories." Czechoslovak Mathematical Journal 73.3 (2023): 765-792. <http://eudml.org/doc/299105>.

@article{Liu2023,
abstract = {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.},
author = {Liu, Jian},
journal = {Czechoslovak Mathematical Journal},
keywords = {periodic complex; orbit category; triangulated hull; derived category; derived equivalence; dg category; Koszul duality},
language = {eng},
number = {3},
pages = {765-792},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Triangulated categories of periodic complexes and orbit categories},
url = {http://eudml.org/doc/299105},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Liu, Jian
TI - Triangulated categories of periodic complexes and orbit categories
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 3
SP - 765
EP - 792
AB - 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.
LA - eng
KW - periodic complex; orbit category; triangulated hull; derived category; derived equivalence; dg category; Koszul duality
UR - http://eudml.org/doc/299105
ER -

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