This article is cited in 29 papers

Locally Scalar Graph Representations in the Category of Hilbert Spaces

S. A. Kruglyak, A. V. Roiter

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: 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, Dynkin graph, Coxeter functor, locally scalar representation, reflection.

UDC: 519.1

Received: 15.07.2003

DOI: 10.4213/faa37

 English version: Functional Analysis and Its Applications, 2005, 39:2, 91–105

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