%0 Journal Article
%T Locally-scalar representations of graphs in the category of Hilbert spaces
%A S. A. Kruglyak
%A A. V. Roiter
%J Mathematics
%D 2003
%I arXiv
%X In this paper authors consider representations of graphs in Hilbert spaces applying a restriction of local scalarity on them. It enables to obtain a theory, similar to the classical theory of representations of graphs in vector spaces. In particular, it is obtained a theorem analogous to the well-known Gabriel theorem: a connected finite graph (wood) is finitely representable in the category of Hilbert spaces if and only if it is a Dynkin graph.
%U http://arxiv.org/abs/math/0307163v2