In the present paper we introduce the notion of representations of a bush which is a generalization of matrix problems (self-reproducing systems) introduced by Nazarova and Roiter. We show that the problem of classifying representations of clannish algebras come down to such generalized matrix problems. Based on the classification of Crawley-Boevey, we provide a description of indecomposable representations of bushes over any field. The proof is based on a categorical formulation of the matrix reduction of Nazarova and Roiter.
Cite this article
B. Deng, On a problem of Nazarova and Roiter. Comment. Math. Helv. 75 (2000), no. 3, pp. 368–409DOI 10.1007/S000140050132