Tilting theory and functor categories I. Classical tilting

Details Tilting theory and functor categories I. Classical tilting Tilting theory and functor categories I. Classical tilting

2011-10-21

arxiv.org/abs/1110.4785v1

Mathematics

Representation Theory

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Scientific paper

Tilting theory has been a very important tool in the classification of finite dimensional algebras of finite and tame representation type, as well as, in many other branches of mathematics. Happel [Ha] proved that generalized tilting induces derived equivalences between module categories, and tilting complexes were used by Rickard [Ri] to develop a general Morita theory of derived categories. In the other hand, functor categories were introduced in representation theory by M. Auslander and used in his proof of the first Brauer- Thrall conjecture and later on, used systematically in his joint work with I. Reiten on stable equivalence and many other applications. Recently, functor categories were used to study the Auslander- Reiten components of finite dimensional algebras. The aim of the paper is to extend tilting theory to arbitrary functor cate- gories, having in mind applications to the functor category Mod(mod{\Lambda}), with {\Lambda} a finite dimensional algebra.

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