Phases of Stable Representations of Euclidean and Wild Quivers  

作　　者：Magnus Engenhorst 

机构地区：[1]Deutsche Postbank AG,Bundeskanzlerplatz 6,Bonn 53113,Germany

出　　处：《Algebra Colloquium》2024年第3期505-524,共20页代数集刊（英文版）

摘　　要：We consider stable representations of non-Dynkin quivers with respect to a central charge.These attract a lot of interest in mathematics and physics since they can be identified with so-called BPS states.Another motivation is the work of Dimitrov et al.on the phases of stable representations of the generalized Kronecker quiver.One aim is to explain for general Euclidean and wild quivers the behavior of phases of stable representations well known in some examples.In addition,we study especially the behavior of preinjective,postprojective and regular indecomposable modules.We show that the existence of a stable representation with self-extensions implies the existence of infinitely many stables without self-extensions for rigid central charges.In this case the phases of the stable representations approach one or two limit points.In particular,the phases are not dense in two arcs.The category of representations of acyclic quivers is a special case of rigid Abelian categories which show this behavior for rigid central charges.

关 键 词：stable representation Euclidean quiver wild quiver Abelian category triangulated category 

分 类 号：O154[理学—数学]