Categorical construction of A,D,E root systems

Details Categorical construction of A,D,E root systems Categorical construction of A,D,E root systems

2010-07-15

arxiv.org/abs/1007.2623v2

Mathematics

Representation Theory

25 pages, 3 figures v2: corrected typos, corrected minor errors

Scientific paper

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.

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