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

2003/07/11 by S. A. Kruglyak, Kruglyak, S. A., A. V. Roiter +2 · 3 citations
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Representation Theory (math.RT) #Topological and Geometric Data Analysis #math.RT

paper · pdf · doi:10.48550/arxiv.math/0307163

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

openalex publication_date 2003/07/11 · arxiv created 2003/09/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Indecomposable representations of quivers on infinite-dimensional Hilbert spaces
• Unbounded strongly irreducible operators and transitive representations of quivers on infinite-dimensional Hilbert spaces
• Separating Functions, Spectral Graph Theory and Locally Scalar Representations in Hilbert Spaces

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