  In Quantum Mechanics operators must be hermitian and, in a direct product
space, symmetric. These properties are saved by Lie algebra operators but not
by those of quantum algebras. A possible correspondence between observables and
quantum algebra operators is suggested by extending the definition of matrix
elements of a physical observable, including the eventual projection on the
appropriate symmetric space. This allows to build in the Lie space of
representations one-parameter families of operators belonging to the enveloping
Lie algebra that satisfy an approximate symmetry and have the properties
required by physics.
