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TILTING MODULES ARISING FROM RING EPIMORPHISMS LIDIA ANGELERI HUGEL AND JAVIER SANCHEZ
 

Summary: TILTING MODULES ARISING FROM RING EPIMORPHISMS
LIDIA ANGELERI H¨UGEL AND JAVIER S´ANCHEZ
Abstract. We show that a tilting module T over a ring R admits an ex-
act sequence 0 R T0 T1 0 such that T0, T1 Add(T) and
HomR(T1, T0) = 0 if and only if T has the form S S/R for some injec-
tive ring epimorphism : R S with the property that TorR
1 (S, S) = 0 and
pdSR 1. We then study the case where is a universal localization in the
sense of Schofield [Sch85]. Using results from [CB91], we give applications to
tame hereditary algebras and hereditary noetherian prime rings. In particular,
we show that every tilting module over a Dedekind domain or over a classical
maximal order arises from universal localization.
Introduction
Tilting theory started in the early eighties in representation theory of finite
dimensional algebras as a tool to relate two module categories via functors inducing
crosswise equivalences between certain parts of both categories. Nowadays tilting
plays an important role in various branches of modern algebra, ranging from Lie
theory and algebraic geometry to homotopical algebra. We refer to [AHKH06] for
a survey on such developments.
In this paper, we will consider (large) tilting modules over an arbitrary ring R,

  

Source: Angeleri Hügel, Lidia - Dipartimento di Informatica, Universita` di Verona

 

Collections: Mathematics