A Realization of the W_(1+∞) Algebra and Its n-Algebra

We consider a realization of the W_(1+∞) algebra and investigate its n-algebra, which is different from the n-algebra of Zhang et al. 2016 arXiv:1606.07570 v2] It is found that the generators W_m~s with any fixed superindex s ≥ 1 yield the null sub-2 s-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+∞) algebra and null n-algebras.