A Realization of the W_1+\infty Algebra and Its n-Algebra

We consider a realization of the W_1+\infty algebra and investigate its n-algebra, which is different from the n-algebra of Zhang et al. 2016 arXiv:1606.07570v2 It is found that the generators W_m^s with any fixed superindex s\geqslant 1 yield the null sub-2s-algebra. The nontrivial sub-4-algebra and Virasoro–Witt 3-algebra are presented. Moreover, we extend the generators to the multi-variables case. These generators also yield the W_1+\infty algebra and null n-algebras.