On Regular Locally Scalar Representations of Graph $\widetilde{D}_4$ in Hilbert Spaces
We classify regular locally scalar (= orthoscalar) representations of graph $\widetilde{D}_4$ in Hilbert spaces
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arXiv subjects
S. A. Kruglyak
Publications and source records attributed to S. A. Kruglyak.
On the indecomposability in the category of representations of a quiver and in its subcategory of orthoscalar representations
One can regard the category of represenations of quivers in Hilbert spaces as a subcategory in the category of all representations, and at that objects, which are indecomposable in the subcategory, become in general decomposable in the ``larger'' category. We prove that it does not happen with indecomposable locally scalar representations of a quiver.
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Matrix Problems in Hilbert Spaces
We consider matrix problems in Hilbert spaces (orthoscalar representations of quivers and posets). A criterion of tameness of the problem of classification of indecomposable orthoscalar representations of a quiver is given.
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Locally-scalar representations of graphs in the category of Hilbert spaces
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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