ON A FERMIONIC REALIZATIONS OF W-TYPE SYMMETRIES

The simplest W-type algebra is considered, which includes spin-3/2 and 1 currents, with the aim of finding all its realizations in the free fermion theory through the currents of the type gamma(i1 ... i2s) psi( i1) ... psi(i2s). The solution of this problem appears to be related t o some problem in the theory of Lie algebras, and we give a classifica tion of the solutions for gamma tensors, which turn out to be connecte d with structure constants of Lie algebras. This is in parallel with p reviously known similar bosonic construction, connected with symmetric counterpart of the Lie algebras - the Jordan algebras.