On the indecomposability in the category of representations of a quiver   and in its subcategory of orthoscalar representations
  One can regard the category of represenations of quivers in Hilbert spaces as a subcategory in the category of all representations, and at that objects, which are indecomposable in the subcategory, become in general decomposable in the ``larger'' category. We prove that it does not happen with indecomposable locally scalar representations of a quiver. 
S. A. Kruglyak, L. A. Nazarova, A. V. Roiter