  In this note we present an explicit realization of the affine vertex algebra
$V^{cri}(\frak{gl}(1 \vert 1)) $ inside of the tensor product $F\otimes M$
where $F$ is a fermionic verex algebra and $M$ is a commutative vertex algebra.
This immediately gives an alternative description of the center of
$V^{cri}(\frak{gl}(1 \vert 1) ) )$ as a subalgebra $M _ 0$ of $M$. We
reconstruct the Molev-Mukhin formula for the Hilbert-Poincare series of the
center of $V^ {cri}(\frak{gl}(1 \vert 1) )$. Moreover, we construct a family of
irreducible $V^{cri}(\frak{gl}(1 \vert 1))$ -modules realized on $F$ and
parameterized by $\chi^+, \chi ^- \in {\Bbb C}((z)). $ We propose a
generalization of $V^ {cri}(\frak{gl}(1 \vert 1))$ as a critical level version
of the super $\mathcal W_{1+\infty}$ vertex algebra.
