Indecomposable representations of quivers on infinite-dimensional Hilbert spaces

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

2007-07-06

arxiv.org/abs/0707.0966v2

Mathematics

Operator Algebras

34 pages

Scientific paper

We study indecomposable representations of quivers on separable infinite-dimensional Hilbert spaces by bounded operators. We consider a complement of Gabriel's theorem for these representations. Let $\Gamma$ be a finite, connected quiver. If its underlying undirected graph contains one of extended Dynkin diagrams $\tilde{A_n} (n \geq 0)$, $\tilde{D_n} (n \geq 4)$, $\tilde{E_6}$,$\tilde{E_7}$ and $\tilde{E_8}$, then there exists an indecomposable representation of $\Gamma$ on separable infinite-dimensional Hilbert spaces.

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