2015/10/01 by Ortiz-Morales, M.
#FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1510.00320
Quasi-hereditary were introduced by L. Scott \citeScott, CPS1,CPS2 in order to deal highest weight categories as they arise in the representation theory of semi-simple complex Lie algebras and algebraic groups, and they have been a very important tool in the study of finite-dimensional algebras. On the other hand, functor categories were introduced in representation theory by M. Auslander [A], [AQM] and used in his proof of the first Brauer-Thrall conjecture [A2] and later on used systematically in his joint work with I. Reiten on stable equivalence [AR], [AR2] and many other applications. Recently, functor categories were used in [MVS3] to study the Auslander-Reiten components of finite-dimensional algebras. The aim of the paper is to introduce the concept of quasi-hereditary category, and we can think of the components of the Auslander-Reiten components as quasi-hereditary categories. In this way, we have applications to the functor category Mod(C ), with \mathcal C a component of the Auslander-Reiten quiver.