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

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.

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

References in corpus (1)

• Unitary and Euclidean representations of a quiver

Cited by in corpus (8)

• On *-representations of a certain class of algebras related to a graph
• Special characters on star graphs and representations of $\ast$-algebras
• Matrix Problems in Hilbert Spaces
• Separating Functions, Spectral Graph Theory and Locally Scalar Representations in Hilbert Spaces
• On Regular Locally Scalar Representations of Graph ${\tilde{D}}_4$ in Hilbert Spaces
• Strongly irreducible operators and indecomposable representations of quivers on infinite-dimensional Hilbert spaces
• Indecomposable representations of quivers on infinite-dimensional Hilbert spaces
• On the indecomposability in the category of representations of a quiver and in its subcategory of orthoscalar representations