Hereditary triangulated categories
نویسندگان
چکیده
منابع مشابه
Objects in Triangulated Categories
We introduce the Calabi-Yau (CY) objects in a Hom-finite Krull-Schmidt triangulated k-category, and notice that the structure of the minimal, consequently all the CY objects, can be described. The relation between indecomposable CY objects and Auslander-Reiten triangles is provided. Finally we classify all the CY modules of selfinjective Nakayama algebras, determining this way the self-injectiv...
متن کاملHeller triangulated categories
Let E be a Frobenius category, let E denote its stable category. The shift functor on E induces a first shift functor on the category of acyclic complexes with entries in E by pointwise application. Shifting a complex by 3 positions yields a second shift functor on this category. Passing to the quotient modulo split acyclic complexes, Heller remarked that these two shift functors become isomorp...
متن کاملStratifying Triangulated Categories
A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences which follow when T is stratified by R. Among them are a classification of the localizing subcategories of T in terms of subsets of the set of prime ideals in...
متن کاملOn Triangulated Orbit Categories
We show that the category of orbits of the bounded derived category of a hereditary category under a well-behaved autoequivalence is canonically triangulated. This answers a question by Aslak Buan, Robert Marsh and Idun Reiten which appeared in their study [8] with M. Reineke and G. Todorov of the link between tilting theory and cluster algebras (cf. also [16]) and a question by Hideto Asashiba...
متن کاملQuotient Triangulated Categories
For self-orthogonal modules T , the quotient triangulated categories D(A)/K(addT ) are studied, in particular, their relations with the stable categories of some Frobenius categories are investigated. New descriptions of the singularity categories of Gorenstein algebras are obtained; and the derived categories of Gorenstein algebras are explicitly given, inside the stable categories of the grad...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Noncommutative Geometry
سال: 2018
ISSN: 1661-6952
DOI: 10.4171/jncg/311