*Article* **Semiheaps and Ternary Algebras in Quantum Mechanics Revisited**

**Andrew James Bruce**

> Department of Mathematics, The Computational Foundry, Swansea University Bay Campus, Fabian Way, Swansea SA1 8EN, UK; andrewjamesbruce@googlemail.com

**Abstract:** 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.

**Keywords:** semiheaps; ternary algebras; para-associativity; quantum mechanics
