The structure of the $$\mathcal{N}=4$$ supersymmetric linear $$W_{\infty }[\lambda ]$$ algebra

Abstract For the vanishing deformation parameter $$\lambda $$ λ , full structure of (anti)commutator relations in $$\mathcal{N}=4$$ N = 4 supersymmetric linear $$W_{\infty }[\lambda =0]$$ W ∞ [ 0 ] algebra is obtained for arbitrary weights $$h_1$$ h 1 and $$h_2$$ 2 currents appearing on left hand sides these (anti)commutators. The $$w_{1+\infty }$$ w + can be seen from this by taking limit other q with proper contractions currents. nonzero complete ]$$ determined weight together constraint $$h_1-3 \le h_2 h_1+1$$ - 3 ≤ . additional structures right (anti)commutators, compared to above =0$$ case, arise where outside region.