  We re-examine the appearance of semiheaps and (para-associative) ternary
algebras in quantum mechanics. In particular, we review the construction of a
semiheap on a Hilbert space and the set of bounded operators on a Hilbert
space. The new aspect of this work is a discussion of how symmetries of a
quantum system induce homomorphisms of the relevant semiheaps and ternary
algebras.
