  With his Clifford algebra of differential forms, Kaehler's algebra addresses
the overlooked manifestation of symmetry in the solutions of exterior systems.
In this algebra, solutions with a given symmetry are members of left ideals
generated by corresponding idempotents. These combine with phase factors to
take care of all the dependence of the solution on $x^{i}$ and $% dx^{i}$ for
each $\partial /\partial x^{i}=0$ symmetry. The maximum number of idempotents
(each for a one-parameter group) that can, therefore, go into a solution is the
dimensionality $n$ of the space. This number is further limited by
non-commutativity of idempotents.
  We consider the tensor product of Kaehler algebra with tangent Clifford
algebra, i.e. of valuedness. It has a commutative subalgebra of "mirror
elements", i.e. where the valuedness is dual to the differential form (like in
$dx\mathbf{i}$, but not in $dx\mathbf{j}$). It removes the aforementioned
limitation in the number of idempotent factors that can simultaneously go into
a solution.
  In the Kaehler calculus, which is based on the Kaehler algebra, total angular
momentum is linear in its components, even it is not valued in tangent algebra.
In particular, it is not a vector operator.
  We carry Kaehler's treatment over to the aforementioned commutative algebra.
Non-commutativity thus ceases to be a limiting factor in the formation of
products of idempotents representing each a one-parameter symmetry. The
interplay of factors that emerges in the expanded set of such products is
inimical to operator theory. For practical reasons, we stop at products
involving three one-parameter idempotents ---henceforth call ternary--- even
though the dimensionality of the all important spacetime manifold allows for
four of them.
