The Graded Center of a Triangulated Category
نویسندگان
چکیده
With applications in mind to the representations and cohomology of block algebras, we examine elements of the graded center of a triangulated category when the category has a Serre functor. These are natural transformations from the identity functor to powers of the shift functor that commute with the shift functor We show that such natural transformations which have support in a single shift orbit of indecomposable objects are necessarily of a kind previously constructed by Linckelmann. Under further conditions, when the support is contained in only finitely many shift orbits, sums of transformations of this special kind account for all possibilities. Allowing infinitely many shift orbits in the support, we construct elements of the graded center of the stable module category of a tame group algebra of a kind that cannot occur with wild block algebras. We use functorial methods extensively in the proof, developing some of this theory in the context of triangulated categories.
منابع مشابه
On the Center of a Triangulated Category
We discuss some basic properties of the graded center of a triangulated category and compute examples arising in representation theory of finite dimensional algebras.
متن کاملDerived 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 triangulated category of singularities of the fiber of W over zero. We also proved that the category of graded D-branes of type B in such LG-models is connected by a fully faithful functor with the derived category of coherent sheaves on the...
متن کاملSupport via central ring actions
The notions of central ring actions and support in triangulated categories have proved quite fruitful recently, cf. [1], [2], [3], [4]. They unify ideas and techniques from group cohomology, commutative ring theory (complete intersections) and Hochschild cohomology. This brief survey is an introduction to the basic concepts. Let T be a triangulated category with suspension functor Σ. A subcateg...
متن کاملGraded B-branes on Simple Singularities
We prove the relation between the triangulated categories of graded B-branes on simple singularities and the derived categories of representations of Dynkin quivers. The proof is based on the theory of weighted projective lines by Geigle and Lenzing and Orlov’s theorem on the relation between triangulated categories of graded B-branes and the derived category of coherent sheaves.
متن کاملKoszul Differential Graded
The concept of Koszul differential graded algebra (Koszul DG algebra) is introduced. Koszul DG algebras exist extensively, and have nice properties similar to the classic Koszul algebras. A DG version of the Koszul duality is proved. When the Koszul DG algebra A is AS-regular, the Ext-algebra E of A is Frobenius. In this case, similar to the classical BGG correspondence, there is an equivalence...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015