Geodesic
Triangulated categories of periodic complexes and orbit categories
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 765-792.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
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 
@article{10_21136_CMJ_2023_0234_22,
     author = {Liu, Jian},
     title = {Triangulated categories of periodic complexes and orbit categories},
     journal = {Czechoslovak Mathematical Journal},
     pages = {765--792},
     publisher = {mathdoc},
     volume = {73},
     number = {3},
     year = {2023},
     doi = {10.21136/CMJ.2023.0234-22},
     mrnumber = {4632857},
     zbl = {07729537},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0234-22/}
}
TY  - JOUR
AU  - Liu, Jian
TI  - Triangulated categories of periodic complexes and orbit categories
JO  - Czechoslovak Mathematical Journal
PY  - 2023
SP  - 765
EP  - 792
VL  - 73
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0234-22/
DO  - 10.21136/CMJ.2023.0234-22
LA  - en
ID  - 10_21136_CMJ_2023_0234_22
ER  - 
%0 Journal Article
%A Liu, Jian
%T Triangulated categories of periodic complexes and orbit categories
%J Czechoslovak Mathematical Journal
%D 2023
%P 765-792
%V 73
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0234-22/
%R 10.21136/CMJ.2023.0234-22
%G en
%F 10_21136_CMJ_2023_0234_22
Liu, Jian. Triangulated categories of periodic complexes and orbit categories. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 765-792. doi : 10.21136/CMJ.2023.0234-22. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0234-22/

Cité par Sources :