  The Levi-Malcev decomposition is applied to bosonic models of quantum
mechanics based on unitary Lie algebras u(2), u(2)+u(2), u(3) and u(4) to
clearly disentangle semisimple subalgebras. The theory of weighted Dynkin
diagrams is then applied to identify conjugacy classes of relevant A_1
subalgebras allowing to introduce a complete classification of new angular
momentum non conserving (AMNC) dynamical symmetries. The tensor analysis of the
whole algebra based on the new "angular momentum" operators reveals unexpected
spinors to occur in purely bosonic models. The new chains of subalgebra can be
invoked to set up ANMC bases for diagonalization.
