Equivalences Induced by Infinitely Generated Tilting Modules
نویسنده
چکیده
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.
منابع مشابه
Infinite Dimensional Tilting Modules and Cotorsion Pairs
Classical tilting theory generalizes Morita theory of equivalence of module categories. The key property – existence of category equivalences between large full subcategories of the module categories – forces the representing tilting module to be finitely generated. However, some aspects of the classical theory can be extended to infinitely generated modules over arbitrary rings. In this paper,...
متن کاملAll Tilting Modules Are of Finite Type
We prove that any infinitely generated tilting module is of finite type, namely that its associated tilting class is the Ext-orthogonal of a set of modules possessing a projective resolution consisting of finitely generated projective modules.
متن کاملTilting Selfinjective Algebras and Gorenstein Orders
BY Rickard's fundamental theorem [8], the rings which are derived equivalent to a ring A are precisely the endomorphism rings of tilting complexes over A. A tilting complex T is a finitely generated complex of finitely generated projective modules, which does not admit selfextensions and which has the property that the smallest triangulated subcategory of D(A) which contains T also contains all...
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 کاملTilting Theory for Coherent Rings and Almost Hereditary Noetherian Rings
We generalize two major ways of obtaining derived equivalences, the tilting process by Happel, Reiten and Smalø and Happel’s Tilting Theorem, to the setting of finitely presented modules over right coherent rings. Moreover, we extend the characterization of quasi–tilted artin algebras as the almost hereditary ones to all right noetherian rings. We also give a streamlined and general presentatio...
متن کامل