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
SN - 0022-1236
VL - 256
SP - 959
EP - 991
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 4
ER -