Scalar endomorphisms obstruct a split extension
= Scalar endomorphisms obstruct a split extension
If a representation has one-dimensional <endomorphism> algebra, it cannot be a <direct sum> of two nonzero invariant subspaces: the two coordinate projections would be independent <endomorphisms>. This obstruction does not require either summand to be irreducible, and does not assert that scalar <endomorphisms> alone imply irreducibility.