Indecomposable representations of quivers on infinite-dimensional Hilbert spaces

Masatoshi Enomoto, Yasuo Watatani

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)


    We study indecomposable representations of quivers on separable infinite-dimensional Hilbert spaces by bounded operators. We exhibit several concrete examples and investigate duality theorem between reflection functors. We also show a complement of Gabriel's theorem. Let Γ be a finite, connected quiver. If its underlying undirected graph contains one of extended Dynkin diagrams over(A, ̃)n(n ≥ 0), over(D, ̃)n(n ≥ 4), over(E, ̃)6, over(E, ̃)7 and over(E, ̃)8, then there exists an indecomposable representation of Γ on separable infinite-dimensional Hilbert spaces.

    Original languageEnglish
    Pages (from-to)959-991
    Number of pages33
    JournalJournal of Functional Analysis
    Issue number4
    Publication statusPublished - Feb 15 2009

    All Science Journal Classification (ASJC) codes

    • Analysis


    Dive into the research topics of 'Indecomposable representations of quivers on infinite-dimensional Hilbert spaces'. Together they form a unique fingerprint.

    Cite this