On a problem of Nazarova and Roiter | Zendy

Bin Deng | Zendy

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On a problem of Nazarova and Roiter

Author(s) -

Bin Deng

Publication year - 2000

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/s000140050132

Subject(s) - mathematics , indecomposable module , generalization , categorical variable , algebra over a field , matrix (chemical analysis) , reduction (mathematics) , field (mathematics) , pure mathematics , mathematical analysis , statistics , materials science , geometry , composite material

. 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.

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