THE FULL STRUCTURE OF QUANTUM N=2 SUPER-$W_3^{\left( 2 \right)} $ ALGEBRA

We present the complete structure of the nonlinear N=2 super extension of Polyakov-Bershadsky, $W_3^{\left( 2 \right)} $, algebra with the generic central charge c, at the quantum level. It contains two extra pairs of fermionic currents with integer spins 1 and 2, besides the currents of N=2 superconformal and $W_3^{\left( 2 \right)} $ algebras. For c→∞ limit, the algebra reduces to the classical one, which has been studied previously. The “hybrid” field realization of this algebra is also discussed.