2011/10/21 by Roberto Martínez-Villa, Martínez-Villa, R., M. Ortiz-Morales +1
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1110.4785
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(modΛ), with Λ a finite dimensional algebra.