  We define the Wajsberg-center and the OML-center of a quantum-Wajsberg
algebra, and study their structures. We prove that the Wajsberg-center is a
Wajsberg subalgebra of a quantum-Wajsberg algebra, and that it is a
distributive sublattice of its corresponding poset. If the quantum-Wajsberg
algebra is quasi-linear, we show that the Wajsberg-center is a linearly ordered
Wajsberg algebra. We also show that the lattice subreduct of the
Wajsberg-center is a Kleene algebra. Furthermore, we prove that the OML-center
is an orthomodular lattice, and the orthomodular lattices form a subvariety of
the variety of quantum-Wajsberg algebras.
