The $\mathcal{N}=2,4$ Supersymmetric Linear $W_{\infty }[\lambda ]$ Algebras for Generic $\lambda$ Parameter

Changhyun Ahn, Man Hea Kim

The four different kinds of currents are given by the multiple $(\beta ,\gamma )$ and $(b,c)$ ghost systems with a multiple product of derivatives. We determine their complete algebra where t…