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

S. A. Kruglyak; A. V. Roiter

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arXiv · math/0307163

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

S. A. Kruglyak·A. V. Roiter

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Abstract

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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BibTeX RIS

S. A. Kruglyak, A. V. Roiter. 2003-09-07. Locally-scalar representations of graphs in the category of Hilbert spaces. https://arxiv.org/abs/math/0307163

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