  It is first shown that the scalar product on any orthogonal space (V, g)
allows one to define linear isomorphisms of the vector spaces of bivectors and
2-forms on V with the underlying vector spaces of the Lie algebra so(p, q) and
its dual, respectively. When those isomorphisms are applied to the
electromagnetic excitation bivector and field strength 2-form, resp., one can
associate various algebraic constructions that pertain to them as bivector
fields and 2-forms with corresponding constructions in terms of so(1, 3) and
its dual. The subsequent association with corresponding things in line geometry
will then become straightforward. In particular, the fields can be represented
by motors, such as screws and wrenches, while the Cartan-Killing form on so(1,
3) is isometric to the scalar product on bivectors that gives the Klein
quadric. When the space of bivectors (and therefore the space of 2-forms) is
given an almost-complex structure (and therefore, a complex structure), one can
also represent most of the constructions on the former and its dual in terms of
so(3; C) and its dual.
