  We explore some explicit representations of a certain stable deformed algebra
of quantum mechanics, considered by R. Vilela Mendes, having a fundamental
length scale. The relation of the irreducible representations of the deformed
algebra to those of the (limiting) Heisenberg algebra is discussed, and we
construct the generalized harmonic oscillator Hamiltonian in this framework. To
obtain local currents for this algebra, we extend the usual nonrelativistic
local current algebra of vector fields and the corresponding group of
diffeomorphisms, modeling the quantum configuration space as a commutative
spatial manifold with one additional dimension.
