Tidsperiod: 2015-01-01 till 2018-12-31
Projektledare: Martin Herschend
Budget: 3 447 000 SEK
This research project aims to study several related topics in higher dimensional Auslander-Reiten theory. Classical Auslander-Reiten theory is an important tool in representation theory of associative algebras, which is a subject connecting various areas, such as algebra, geometry and combinatorics. Higher dimensional Auslander-Reiten theory is particularly well suited to treat algebras of global dimension n, just as the classical theory is for hereditary algebras. Many classical concepts have higher dimensional analogues, e.g., n-representation finite and n-representation infinite algebras correspond to the classical division into finite and infinite representation type. An overall aim of this project is to further explore such higher dimensional analogues.One aim is to study 2-representation finite and infinite algebras using selfinjective respectively 3-Calabi-Yau quivers with potential and cuts. These combinatorial methods will allow us to construct families of examples of such algebras and study important questions, such as when they are derived equivalent. We further aim to generalize these methods to n > 2.We will also investigate topics of more geometric origin. For instance, we will study 2-representation finite algebras coming from one-dimensional surface singularities and n-canonical algebras coming from certain weighted projective spaces. Contributing to this connection between algebra and geometry is one of the most significant goals of this project.