Representation of Quivers
This chapter introduces another aspect of the current research on representation of algebras. This Une of work began with the papers  and  of P. Gabriel. He gave an explicit construction of the indecomposable modules for certain finite dimensional F-algebras. The most surprising part of Gabriel’s result is a link between the representation theory of algebras and the Dynkin diagrams that occur in the study of semisimple Lie algebras. This relation between associative and Lie algebras was clarified by Bernstein, Gel’fand and Ponomarev in ; they showed that many algebraic problems can be formulated as questions about the representations of quivers. The characterization of finite representation type for certain associative algebras and the structure theory of semisimple Lie algebras are such problems.
KeywordsDisjoint Union Isomorphism Class Representation Type Dynkin Diagram Indecomposable Module
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