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Funktsional'nyi Analiz i ego Prilozheniya, 2005, Volume 39, Issue 2, Pages 13–30
DOI: https://doi.org/10.4213/faa37 (Mi faa37) 		 
This article is cited in 29 scientific papers (total in 30 papers)

Locally Scalar Graph Representations in the Category of Hilbert Spaces

S. A. Kruglyak, A. V. Roiter

Institute of Mathematics, Ukrainian National Academy of Sciences
Full-text PDF (282 kB) Citations (30)
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DOI: https://doi.org/10.4213/faa37
Abstract: The condition of being locally scalar is imposed on graph (or quiver) representations in the category of Hilbert spaces. Under this condition, reflection and Coxeter functors are constructed in categories of such representations and used to prove an analog of the Gabriel theorem.
Keywords: quiver (graph) representation, unitary equivalence, Hilbert space, Dynkin graph, Coxeter functor, locally scalar representation, reflection.
Received: 15.07.2003
English version:
Functional Analysis and Its Applications, 2005, Volume 39, Issue 2, Pages 91–105
DOI: https://doi.org/10.1007/s10688-005-0022-8
Bibliographic databases:
Document Type: Article
UDC: 519.1
Language: Russian
Citation: S. A. Kruglyak, A. V. Roiter, “Locally Scalar Graph Representations in the Category of Hilbert Spaces”, Funktsional. Anal. i Prilozhen., 39:2 (2005), 13–30; Funct. Anal. Appl., 39:2 (2005), 91–105
Citation in format AMSBIB
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    • This publication is cited in the following 30 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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