Orthoscalar quiver representations corresponding to extended Dynkin graphs in the category of Hilbert spaces |
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Authors: | S A Kruglyak L A Nazarova A V Roiter |
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Institution: | 1.Institute of Mathematics,National Academy of Sciences of Ukraine,Moscow,Russia |
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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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Keywords: | |
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