Derived equivalences induced by nonclassical tilting objects
نویسندگان
چکیده
منابع مشابه
Universal Derived Equivalences of Posets of Cluster Tilting Objects
We show that for two quivers without oriented cycles related by a BGP reflection, the posets of their cluster tilting objects are related by a simple combinatorial construction, which we call a flip-flop. We deduce that the posets of cluster tilting objects of derived equivalent path algebras of quivers without oriented cycles are universally derived equivalent. In particular, all Cambrian latt...
متن کاملEquivalences Induced by Infinitely Generated Tilting Modules
We generalize Brenner and Butler’s Theorem as well as Happel’s Theorem on the equivalences induced by a finitely generated tilting module over Artin algebras, to the case of an infinitely generated tilting module over an arbitrary associative ring establishing the equivalences induced between subcategories of module categories and also at the level of derived categories.
متن کاملUniversal Derived Equivalences of Posets of Tilting Modules
We show that for two quivers without oriented cycles related by a BGP reflection, the posets of their tilting modules are related by a simple combinatorial construction, which we call flip-flop. We deduce that the posets of tilting modules of derived equivalent path algebras of quivers without oriented cycles are universally derived equivalent.
متن کاملSILTING OBJECTS, t-STRUCTURES AND DERIVED EQUIVALENCES
This note is an extended abstract of my talk given in the conference: “Maurice Auslander Distinguished Lectures and International Conference”, April 29 May 4, 2015. It is based on [6] which is joint work with Jorge Vitória.
متن کاملDerived Equivalences of Triangular Matrix Rings Arising from Extensions of Tilting Modules
A triangular matrix ring Λ is defined by a triplet (R, S, M) where R and S are rings and RMS is an S-R-bimodule. In the main theorem of this paper we show that if TS is a tilting S-module, then under certain homological conditions on the S-module MS , one can extend TS to a tilting complex over Λ inducing a derived equivalence between Λ and another triangular matrix ring specified by (S′, R, M ...
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: Proceedings of the American Mathematical Society
سال: 2016
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13368