This article is cited in 5 papers

Orthoscalar quiver representations corresponding to extended Dynkin graphs in the category of Hilbert spaces

S. A. Kruglyak, L. A. Nazarova, A. V. Roiter

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: It is known that finitely representable quivers correspond to Dynkin graphs and tame quivers correspond to extended Dynkin graphs. In an earlier paper, the authors generalized some of these results to locally scalar (later renamed to orthoscalar) quiver representations in Hilbert spaces; in particular, an analog of the Gabriel theorem was proved. In this paper, we study the relationships between indecomposable representations in the category of orthoscalar representations and indecomposable representations in the category of all quiver representations. For the quivers corresponding to extended Dynkin graphs, the indecomposable orthoscalar representations are classified up to unitary equivalence.

Keywords: quiver, orthoscalar representation, Hilbert space, extended Dynkin graphs, unitary equivalence.

UDC: 519.1

Received: 13.02.2009

DOI: 10.4213/faa2986

 English version: Functional Analysis and Its Applications, 2010, 44:2, 125–138

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