Abstract
As is known, finitely presented quivers correspond to Dynkin graphs (Gabriel, 1972) and tame quivers correspond to extended Dynkin graphs (Donovan and Freislich, Nazarova, 1973). In the article “Locally scalar representations of graphs in the category of Hilberts spaces” (Func. Anal. Apps., 2005), the authors showed a way for carrying over these results to Hilbert spaces, constructed Coxeter functors, and proved an analog of the Gabriel theorem for locally scalar representations (up to unitary equivalence).
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