Abstract spin formalism is introduced to simplify the quantum mechanical description of spins I = 3/2. The approach is based on a factorization of Hilbert space that can be applied to any spin for which 2I + 1 is not a prime number. For I = 3/2, a description in terms of two coupled abstract spins 1/2 is obtained that allows one to make use of the well-established product operator formalism. This approach is applied to the analysis of spin lock of the central transition in a static sample. The treatment is extended to the case of magic angle sample spinning by using Floquet operator formalism [A. Schmidt and S. Vega, J. Chem. Phys. 96, 6895 (1987)]. It is demonstrated that a proper spin lock requires a sample spinning frequency that is larger than the radio frequency held strength. The theoretical results are confirmed by numerical simulations and experiments. The concept of spin locking in the fast-spinning, low-power regime is utilized in a cross polarization experiment on sodium nitrite. Cross polarization from Na-23 to N-15 at a distance of more than 2.6 Angstrom results in an about sevenfold better signal-to-noise ratio than direct polarization.