Indecomposable representations of quivers on infinite-dimensional Hilbert spaces

Masatoshi Enomoto, Yasuo Watatani

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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
Volume256
Issue number4
DOIs
Publication statusPublished - Feb 15 2009

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Quiver
Hilbert space
Dynkin Diagram
Duality Theorems
Bounded Operator
Undirected Graph
Functor
Complement
Theorem

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

Indecomposable representations of quivers on infinite-dimensional Hilbert spaces. / Enomoto, Masatoshi; Watatani, Yasuo.

In: Journal of Functional Analysis, Vol. 256, No. 4, 15.02.2009, p. 959-991.

Research output: Contribution to journalArticle

Enomoto, Masatoshi ; Watatani, Yasuo. / Indecomposable representations of quivers on infinite-dimensional Hilbert spaces. In: Journal of Functional Analysis. 2009 ; Vol. 256, No. 4. pp. 959-991.
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