  The multiple-quantum NMR spectroscopy has an extensive application in
determination of the bio-macro-molecular structures and in the investigation of
the properties of a variety of physical materials. In quantum computation the
multiple-quantum transition processes have been used to construct the quantum
circuits, quantum algorithms, and quantum simulations. The multiple-quantum
operator algebra spaces are closely related to the symmetries of a
multiple-spin quantum system. They may have an important effect on the
multiple-quantum transition processes and the multiple-quantum NMR spectroscopy
of the spin system. Here gives a brief introduction to the multiple-quantum
operator algebra spaces.
