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

Abstract

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