Corpus ID: 237572105

Triangulated categories of periodic complexes and orbit categories

@inproceedings{Liu2021TriangulatedCO,
  title={Triangulated categories of periodic complexes and orbit categories},
  author={Jian Liu},
  year={2021}
}
  • Jian Liu
  • Published 18 September 2021
  • Mathematics
We investigate the triangulated hull of the 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 will correspond to the full subcategory of compact objects of certain triangulated categories of periodic complexes. This specializes to Stai and Zhao’s result when the ring is a finite dimensional algebra with finite global dimension over a field. As the first application… Expand

References

SHOWING 1-10 OF 36 REFERENCES
Homology of perfect complexes
Abstract It is proved that the sum of the Loewy lengths of the homology modules of a finite free complex F over a local ring R is bounded below by a number depending only on R. This result uncovers,Expand
The triangulated hull of periodic complexes
In the terms of an `$n$-periodic derived category', we describe explicitly how the orbit category of the bounded derived category of an algebra with respect to powers of the shift functor embeds inExpand
Higher differential objects in additive categories
Abstract Given an additive category C and an integer n ⩾ 2 . We form a new additive category C [ ϵ ] n consisting of objects X in C equipped with an endomorphism ϵ X satisfying ϵ X n = 0 . First,Expand
On the cyclic homology of exact categories
Abstract The cyclic homology of an exact category was defined by McCarthy (1994) using the methods of Waldhausen (1985). McCarthy's theory enjoys a number of desirable properties, the most basicExpand
Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities
In this paper we establish an equivalence between the category of graded D-branes of type B in Landau–Ginzburg models with homogeneous superpotential W and the triangulated category of singularitiesExpand
Sheaf Cohomology and Free Resolutions over Exterior Algebras
In this paper we derive an explicit version of the Bernstein- Gel'fand-Gel'fand (BGG) correspondence between bounded complexes of coherent sheaves on projective space and minimal doubly infinite freeExpand
Root Categories and Simple Lie Algebras
Abstract By using the T 2 -orbit category of the derived category of a hereditary algebra, which is proved to be a triangulated category too, we give a complete realization of a simple Lie algebra.Expand
RELATIVE HOMOLOGICAL ALGEBRA
Introduction. The main purpose of this paper is to draw attention to certain functors, exactly analogous to the functors "Tor" and "Ext" of Cartan-Eilenberg [2], but applicable to a module theoryExpand
Acyclicity Versus Total Acyclicity for Complexes over Noetherian Rings
It is proved that for a commutative noetherian ring with dualizing complex the homotopy category of projective modules is equivalent, as a triangulated category, to the homotopy category of injectiveExpand
Tilting theory and cluster combinatorics
Abstract We introduce a new category C , which we call the cluster category , obtained as a quotient of the bounded derived category D of the module category of a finite-dimensional hereditaryExpand
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