Tilting Modules and Tilting Torsion Theories
نویسندگان
چکیده
منابع مشابه
Stability conditions, torsion theories and tilting
The space of stability conditions of a triangulated category is naturally partitioned into subsets U(A) of stability conditions with a given heart A. If A has finite length and n simple objects then U(A) has a simple geometry, depending only on n. Furthermore, Bridgeland has shown that if B is obtained from A by tilting at a torsion theory generated by one simple object then the intersection of...
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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 کاملConstructing Tilting Modules
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 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...
متن کاملDimensions of Quantized Tilting Modules
We will follow the notations of [7]. Let (Y,X, . . . ) be a simply connected root datum of finite type. Let p be a prime number bigger than the Coxeter number h. Let ζ be a primitive p-th root of unity in C. Let U be the quantum group with divided powers associated to these data. Let T be the category of tilting modules over U , see e.g. [1]. Recall that any tilting module is a sum of indecompo...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1995
ISSN: 0021-8693
DOI: 10.1006/jabr.1995.1368