Cluster-Tilting Theory
نویسنده
چکیده
Tilting theory provides a good method for comparing two categories, such as module categories of finite-dimensional algebras. For an introduction, see e.g. [A]. BGP reflection functors [BGP] give a way of comparing the representation categories of two quivers, where one is obtained from the other by reversing all of the arrows incident with a sink or source. Auslander, Platzeck and Reiten [APR] showed that the BGP reflection functors can be realised directly as functors of the form Hom(T,−), where T is an APR-tilting module.
منابع مشابه
On Tilting Modules over Cluster-tilted Algebras
In this paper, we show that the tilting modules over a clustertilted algebra A lift to tilting objects in the associated cluster category CH . As a first application, we describe the induced exchange relation for tilting Amodules arising from the exchange relation for tilting object in CH . As a second application, we exhibit tilting A-modules having cluster-tilted endomorphism algebras. Cluste...
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تاریخ انتشار 2008