Quasi-Tilting Modules and Counter Equivalences
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 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 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...
متن کاملRigidity of Tilting Modules
Let Uq denote the quantum group associated with a finite dimensional semisimple Lie algebra. Assume that q is a complex root of unity of odd order and that Uq is obtained via Lusztig’s q-divided powers construction. We prove that all regular projective (tilting) modules for Uq are rigid, i.e., have identical radical and socle filtrations. Moreover, we obtain the same for a large class of Weyl m...
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 ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1997
ISSN: 0021-8693
DOI: 10.1006/jabr.1997.6873