Locally-scalar representations of graphs in the category of Hilbert spaces

Details Locally-scalar representations of graphs in the category of Hilbert spaces Locally-scalar representations of graphs in the category of Hilbert spaces

2003-07-11

arxiv.org/abs/math/0307163v2

Mathematics

Representation Theory

18 pages. Report: International Conference on Algebras, Modules and Rings, Lisbon 2003 (reported by I. Redchuk)

Scientific paper

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.

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