Derived equivalences induced by big cotilting modules
نویسندگان
چکیده
منابع مشابه
Equivalences 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 کاملCotilting Modules and Homological Ring Epimorphisms
We show that every injective homological ring epimorphism f : R → S where SR has flat dimension at most one gives rise to a 1cotilting R-module and we give sufficient conditions under which the converse holds true. Specializing to the case of a valuation domain R, we illustrate a bijective correspondence between equivalence classes of injective homological ring epimorphisms originating in R and...
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 کاملAbstract Elementary Classes Induced by Tilting and Cotilting Modules Have Finite Character
ELEMENTARY CLASSES INDUCED BY TILTING AND COTILTING MODULES HAVE FINITE CHARACTER
متن کاملStatic modules and equivalences
By a well known theorem of K. Morita, any equivalence between full module categories over rings R and S, are given by a bimodule RPS , such that RP is a finitely generated projective generator in R-Mod and S = EndR(P ). There are various papers which describe equivalences between certain subcategories of R-Mod and S-Mod in a similar way with suitable properties of RPS . Here we start from the o...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2014
ISSN: 0001-8708
DOI: 10.1016/j.aim.2014.06.007