  We summarize some previous work on SU(4) describing hadron representations
and transformations as well as its noncompact 'counterpart' SU$*$(4) being the
complex embedding of SL(2,$\mathbb{H}$). So after having related the 16-dim
Dirac algebra to SU$*$(4), on the one hand we have access to real, complex and
quaternionic Lie group chains and their respective algebras, on the other hand
it is of course possible to relate physical descriptions to the respective
representations. With emphasis on the common maximal compact subgroup USp(4),
we are led to projective geometry of real 3-space and various transfer
principles which we use to extend previous work on the rank 3-algebras above.
On real spaces, such considerations are governed by the groups SO($n$,$m$) with
$n+m=6$. The central thread, however, focuses here on line and Complex geometry
which finds its well-known counterparts in descriptions of electromagnetism and
special relativity as well as - using transfer principles - in Dirac, gauge and
quantum field theory. We discuss a simple picture where Complexe of second
grade play the major and dominant r\^{o}le to unify (real) projective geometry,
complex representation theory and line/Complex representations in order to
proceed to dynamics.
