Abstract
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 γi1…i2sψi1 … ψi2s. The solution of this problem appears to be related to some problem in the theory of Lie algebras, and we give a classification of the solutions for γ tensors, which turn out to be connected with structure constants of Lie algebras. This is in parallel with previously known similar bosonic construction, connected with symmetric counterpart of the Lie algebras — the Jordan algebras.
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