CENTRAL EUROPEAN JOURNAL OF PHYSICS, vol.9, no.4, pp.996-1001, 2011 (Journal Indexed in SCI)
We present an algebra generated by a single pair of creation and annihilation operators b and b*. We prove that the algebra has a unique d-dimensional representation. Physically this algebra corresponds to a system where there are at most d - 1 particles in a state with otherwise same quantum numbers.