  We study an important property of shape invariant supersymmetric quantum
mechanical systems. Particularly, we demonstrate that each shape invariant
supersymmetric system can constitute a $Z_3$-graded topological symmetric
algebra. The latter is known to provide topological invariants which are
generalizations of the Witten index. In addition, we relate the $Z_3$-graded
algebra to the generators of the SO(2,1) Lie algebra underlying each shape
invariant system. We generalize the results to the case of sequential shape
invariant systems, in which case we find a sequence of $Z_3$-graded algebras.
Finally, we briefly discuss two systems that are related to shape invariance,
but have different algebraic origin, namely supersymmetric systems with central
charge equipped with an additional symmetry and $Z_3$-graded algebraic systems.
In view of the fact that the shape invariance condition is somewhat an
additional algebraic condition, with no origin to some concrete algebraic
structure, our results might be useful towards this line of research.
