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Orthoscalar quiver representations corresponding to extended Dynkin graphs in the category of Hilbert spaces

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Abstract

It is known that finitely representable quivers correspond to Dynkin graphs and tame quivers correspond to extended Dynkin graphs. In an earlier paper, the authors generalized some of these results to locally scalar (later renamed to orthoscalar) quiver representations in Hilbert spaces; in particular, an analog of the Gabriel theorem was proved. In this paper, we study the relationships between indecomposable representations in the category of orthoscalar representations and indecomposable representations in the category of all quiver representations. For the quivers corresponding to extended Dynkin graphs, the indecomposable orthoscalar representations are classified up to unitary equivalence.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Moscow, Russia

    S. A. Kruglyak, L. A. Nazarova & A. V. Roiter

Authors
  1. S. A. Kruglyak
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  2. L. A. Nazarova
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  3. A. V. Roiter
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Correspondence to S. A. Kruglyak.

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__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 44, No. 2, pp. 57–73, 2010

Original Russian Text Copyright © by S. A. Kruglyak, L. A. Nazarova, and A. V. Roiter

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Kruglyak, S.A., Nazarova, L.A. & Roiter, A.V. Orthoscalar quiver representations corresponding to extended Dynkin graphs in the category of Hilbert spaces. Funct Anal Its Appl 44, 125–138 (2010). https://doi.org/10.1007/s10688-010-0016-z

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  • DOI: https://doi.org/10.1007/s10688-010-0016-z

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