We develop an algorithm for computing the closure of a given nilpotent $G_0$-orbit in $g_1$, where $g_1$ and $G_0$ are coming from a $Z$ or a $Z/mZ$-grading $g= bigoplus g_i$ of a simple complex Lie algebra $g$.
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 iden
tify 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.
