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Mathematics > Representation Theory

arXiv:1007.2623 (math)
[Submitted on 15 Jul 2010 (v1), last revised 28 May 2012 (this version, v3)]

Title:Categorical construction of A,D,E root systems

Authors:Alexander Kirillov Jr, Jaimal Thind
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Abstract:Let \Gamma be 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 \Gamma. Instead of choosing an orientation of \Gamma and studying representations of the associated quiver, we study representations of a canonical quiver \Gammahat associated to \Gamma . This construction is very closely related to the preprojective algebra of \Gamma . In particular, the construction gives a certain periodicity result about the preprojective algebra.
Comments: 25 pages, 3 figures v3: corrected typos, added new reference (see Remark 1.2)
Subjects: Representation Theory (math.RT)
Cite as: arXiv:1007.2623 [math.RT]
  (or arXiv:1007.2623v3 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.1007.2623

Submission history

From: Jaimal Thind [view email]
[v1] Thu, 15 Jul 2010 17:53:29 UTC (28 KB)
[v2] Tue, 17 May 2011 17:58:27 UTC (28 KB)
[v3] Mon, 28 May 2012 18:40:30 UTC (29 KB)
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