Lidia Angeleri Hügel
Tilting Modules over Tame Hereditary Algebras.
Tue, 07/27/2010 - 15:01 — SomNambulAuthors: Lidia Angeleri Hügel, Javier Sánchez
Subjects: Representation Theory
AbstractWe give a complete classification of the infinite dimensional tilting modules
over a tame hereditary algebra R. We start our investigations by considering
tilting modules of the form T=R_U\oplus R_U /R where U is a union of tubes, and
R_U denotes the universal localization of R at U in the sense of Schofield and
Crawley-Boevey. Here R_U/R is a direct sum of the Pr\"ufer modules
corresponding to the tubes in U.Recollements and tilting objects.
Mon, 08/17/2009 - 18:30 — SomNambulAuthors: Lidia Angeleri Hügel, Steffen König, Qunhua Liu
Subjects: Representation Theory
AbstractWe study connections between recollements of the derived category D(Mod-R) of
a ring R and tilting theory. We first provide constructions of tilting objects
from given recollements, recovering several different results from the
literature. Secondly, we show how to construct a recollement from a tilting
module of projective dimension one. Our results will be employed in a
forthcoming paper in order to investigate stratifications of D(Mod-R).- 21 comments
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Tilting modules and universal localization.
Mon, 08/17/2009 - 18:30 — SomNambulAuthors: Lidia Angeleri Hügel, Maria Archetti
Subjects: Representation Theory
AbstractWe show that every tilting module of projective dimension one over a ring R
is associated in a natural way to the universal localization (in the sense of
Schofield) of R at a set of finitely presented modules of projective dimension
one. We then investigate tilting modules arising from universal localization.
Furthermore, we discuss the relationship between universal localization and the
localization given by a perfect Gabriel topology. Finally, we give some
applications to Artin algebras and to Pruefer domains.- 7 comments
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