TY - JOUR

T1 - Indecomposable representations of quivers on infinite-dimensional Hilbert spaces

AU - Enomoto, Masatoshi

AU - Watatani, Yasuo

N1 - Funding Information:
The authors are supported by the Grant-in-Aid for Scientific Research of JSPS.

PY - 2009/2/15

Y1 - 2009/2/15

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jfa.2008.12.011

DO - 10.1016/j.jfa.2008.12.011

M3 - Article

AN - SCOPUS:58149336757

VL - 256

SP - 959

EP - 991

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 4

ER -