$w_{\infty}$ 3-algebra
  We use `lone-star' product of the $W_{\infty}$ generators as well as their commutation relations to obtain a $w_{\infty}$ 3-algebra by applying appropriate double scaling limits on the generators. We show explicitly that "Fundamental Identity Condition" (FI) of 3-algebra is satisfied. 
Shankhadeep Chakrabortty, Alok Kumar, Sachin Jain