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Auslander–Reiten theory for modules of finite complexity over self‐injective algebras
Author(s) -
Kerner Otto,
Zacharia Dan
Publication year - 2011
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdq082
Subject(s) - mathematics , injective function , algebraically closed field , diagram , pure mathematics , graph , component (thermodynamics) , field (mathematics) , algebra over a field , discrete mathematics , physics , thermodynamics , statistics
In this paper, we describe the shapes of the stable components containing modules with finite complexity over a self‐injective finite‐dimensional algebra over an algebraically closed field. We prove that the associated orbit graph of each such component is either a Dynkin diagram (finite or infinite), or an extended Dynkin diagram.