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Let R be a ring. A right R-module U is called Tor-tilting if Cogen(U ) = U , where U R(U, Q/Z) and U = KerTor (U, -). Some characterizations of Tor-tilting = HomZ1+is Tor-tilting if and only if U i...
Stratifications of derived categories from tilting modules over tame hereditary algebras
Adele ring Recollement Stratification Tame hereditary algebra Tilting module Universal localization
2011/8/24
Abstract: n this paper, we consider the endomorphism algebras of infinitely generated tilting modules of the form $R_{\mathcal U}\oplus R_{\mathcal U}/R$ over tame hereditary $k$-algebras $R$ with $k$...
The purpose of this chapter is to give an introduction to the theory of cluster categories and cluster-tilted algebras, with some background on the theory of cluster algebras, which motivated these to...
Good tilting modules and recollements of derived module categories
Commutative algebras Coproducts Derived categories p-adic numbers Recollements Ring epimorphisms Tilting
2011/1/20
Let T be an infinitely generated tilting module of projective dimension at most one over an arbitrary associative ring A, and let B be the endomorphism ring of T.
Tilting and cluster tilting for quotient singularities
Cohen-Macaulay module quotient singularity stable category triangulated category
2011/3/1
We shall show that the stable categories of graded Cohen-Macaulay modules over quotient
singularities have tilting objects. In particular, these categories are triangle equivalent to derived cat-egor...
On tilting complexes providing derived equivalences that send simple-minded objects to simple objects
send simple-minded simple objects
2010/11/22
Given a set of 'simple-minded' objects in a derived category, Rickard constructed a complex, which over a symmetric algebra provides a derived equivalence sending the 'simple-minded' objects to simpl...
From Jantzen to Andersen Filtration via Tilting Equivalence
Jantzen Andersen Filtration via Tilting Equivalence
2010/11/12
The space of homomorphisms from a projective object to a Verma module in category O inherits an induced filtration from the Jantzen filtration on the Verma module. On the other hand there is the Ande...
Graded mutation in cluster categories coming from hereditary categories with a tilting object
Graded mutation cluster categories hereditary categories tilting object
2010/12/13
We present a graded mutation rule for quivers of clustertilted algebras. Furthermore, we give a technique to recover a clustertilting object from its graded quiver in the cluster category of cohX.
We define tilting mutations of symmetric algebras as the endomorphism algebras of Okuyama-Rickard complexes. For Brauer tree algebras, we give an explicit description of the change of
Brauer trees un...