  Quantum algebras (also called quantum groups) are deformed versions of the
usual Lie algebras, to which they reduce when the deformation parameter q is
set equal to unity. From the mathematical point of view they are Hopf algebras.
Their use in physics became popular with the introduction of the q-deformed
harmonic oscillator as a tool for providing a boson realization of the quantum
algebra SUq(2), although similar mathematical structures had already been
known. Initially used for solving the quantum Yang-Baxter equation, quantum
algebras have subsequently found applications in several branches of physics,
as, for example, in the description of spin chains, squeezed states, hydrogen
atom and hydrogen-like spectra, rotational and vibrational nuclear and
molecular spectra, and in conformal field theories. By now much work has been
done on the q-deformed oscillator and its relativistic extensions, and several
kinds of generalized deformed oscillators and SU(2) algebras have been
introduced. Here we shall confine ourselves to a list of applications of
quantum algebras in nuclear structure physics and in molecular physics and, in
addition, a recent application of quantum algebraic techniques to the structure
of atomic clusters will be discussed in more detail.
