Tilting modules and universal localization
نویسندگان
چکیده
منابع مشابه
Tilting Modules and Universal Localization
We show that every tilting module of projective dimension one over a ring R is associated in a natural way to the universal localization R → RU at a set U of finitely presented modules of projective dimension one. We then investigate tilting modules of the form RU ⊕ RU/R. Furthermore, we discuss the relationship between universal localization and the localization R → QG given by a perfect Gabri...
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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 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...
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We investigate the structure of (infinite dimensional) tilting modules over hereditary artin algebras. For connected algebras of infinite representation type with Grothendieck group of rank n, we prove that for each 0 ≤ i < n− 1, there is an infinite dimensional tilting module Ti with exactly i pairwise non-isomorphic indecomposable finite dimensional direct summands. We also show that any ston...
متن کاملTilting Modules in Truncated Categories
We begin the study of a tilting theory in certain truncated categories of modules G(Γ) for the current Lie algebra associated to a finite-dimensional complex simple Lie algebra, where Γ = P × J , J is an interval in Z, and P is the set of dominant integral weights of the simple Lie algebra. We use this to put a tilting theory on the category G(Γ′) where Γ′ = P ′×J , where P ′ ⊆ P is saturated. ...
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ژورنال
عنوان ژورنال: Forum Mathematicum
سال: 2012
ISSN: 1435-5337,0933-7741
DOI: 10.1515/form.2011.080