Chrysostomos Psaroudakis

Monomorphism Categories and Derived Equivalences

Abstract:

The study of monomorphism categories is known to be very useful in connection with classification problems and not only. For an algebra A, the category of monomorphisms over A can be considered as a full subcategory of the modules over the upper triangular matrix algebra with entries the algebra A. It is an exact category in the sense of Quillen and therefore its derived category can be defined. Our aim in this talk is to study the bounded derived category of the monomorphism category of an Artin algebra. In particular, we show how we can realize the bounded derived category of the monomorphism category as a bounded derived category of some abelian (module) category. This is achieved by constructing tilting objects in the bounded derived category of the monomorphism category from tilting modules of the algebra.

This is joint work with Nan Gao.