2010/07/15 by Alexander Kirillov, Alexander Kirillov Jr, Kirillov, Alexander +2
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1007.2623
25 pages, 3 figures v3: corrected typos, added new reference (see Remark 1.2)
openalex publication_date 2010/07/15 · arxiv created 2012/05/28 · arxiv updated 2012/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Γbe a Dynkin diagram of type A,D,E and let R denote the corresponding root system. In this paper we give a categorical construction of R from Γ. Instead of choosing an orientation of Γand studying representations of the associated quiver, we study representations of a canonical quiver \Gammahat associated to Γ. This construction is very closely related to the preprojective algebra of Γ. In particular, the construction gives a certain periodicity result about the preprojective algebra.