Almost extraspecial structures and pseudofermionic operators

Abstract

We survey some recent combinatorial properties, which have been found in the context of the algebras of ladder operators in quantum mechanics. More specifically, we review dynamical systems which have nonselfadjoint Hamiltonians and are subject to a formalization in terms of pseudofermionic operators. For these systems, we detect structural analogies between algebras of pseudofermionic operators and the abstract notion of central product, which was originally studied for finite groups.