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We consider the sl(2) current algebra at level k=-4 when the sl(2) BRSToperator is nilpotent. We formulate a spectral sequence converging to thecohomology of this BRST operator. At the second term of the spectral sequence,we observe an N=4 algebra. This algebra is generated in a c=-2 bosonic stringwhose BRST operator Q_{string} represents the next term in the spectralsequence. We realize the cohomology of the irreducible modules asQ_{string}-primitives of the N=4 singular vectors and point out their relationto Lian--Zuckerman states of c=-2 matter. The relation between sl(2)_{-4} WZWmodel and c=-2 bosonic string is established both at the level of BRSTcohomology and at the level of an explicit operator construction. The relationof the N=4 algebra to the known symmetries of matter+gravity systems is alsoinvestigated.Comment: LaTeX 2.09, 23 pages, no figure

sℓ(2)−4 WZW MODEL AS AN (N=4)-SUPERSYMMETRIC BOSONIC STRING WITH c=−2 MATTER

sℓ(2)₋₄ WZW MODEL AS AN (N=4)-SUPERSYMMETRIC BOSONIC STRING WITH c=−2 MATTER