Geodesic
Locally Scalar Graph Representations in the Category of Hilbert Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 2, pp. 13-30

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The condition of being locally scalar is imposed on graph (or quiver) representations in the category of Hilbert spaces. Under this condition, reflection and Coxeter functors are constructed in categories of such representations and used to prove an analog of the Gabriel theorem.
Keywords: quiver (graph) representation, unitary equivalence, Hilbert space, Coxeter functor, locally scalar representation, reflection.
Mots-clés : Dynkin graph 
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S. A. Kruglyak; A. V. Roiter. Locally Scalar Graph Representations in the Category of Hilbert Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 2, pp. 13-30. http://geodesic.mathdoc.fr/item/FAA_2005_39_2_a1/