The second author is supported by an NSERC Discovery Grant.

Notation {#section1}
========

We briefly review the basic theory of vector superspaces and Lie superalgebras. For more detailed expositions, see for example [ChWabook]{} or [@Musson]. Throughout this article, all vector spaces will be over $\C$. Let $\SVec$ be the symmetric monoidal category of $\Ztwo$-graded vector spaces, where $\Ztwo:=\left\{\eev,\ood\right\}$. Objects of $\SVec$ are of the form $U=U_\eev\oplus U_\ood$. The parity of a homogeneous vector $u\in U$ is denoted by $|u|\in\Ztwo$. For any two $\Ztwo$-graded vector spaces $U$ and $U'$, the vector space $\Hom_\C
(U,U^{\prime})$ is naturally $\Ztwo$-graded, and the morphisms of $\SVec$ are defined by $\Mor_{\SVec}(U,U^{\prime
}):=\Hom_\C
(U,U^{\prime})_\eev$. The symmetry isomorphism of $\SVec$ is defined by $$\label{symisomdf}
\braid_{U,U^{\prime }}:U\otimes U^{\prime }\to U^{\prime }\otimes U \ ,\
u\otimes u^\prime 
\mapsto (-1)^{|u|\cdot |u^{\prime }|}u^{\prime }\otimes u.$$ We remark that throughout this article, the defining relations which involve parities of vectors should first be construed as relations for homogeneous vectors, and then be extended by linearity to arbitrary vectors.

The identity element of the associative superalgebra $
\mathrm{End}_\C(U):=%
\Hom_\C(U,U)
$ will be denoted by $1_U$. Note that $\mathrm{End}_\C(U)$ is a Lie superalgebra with the standard commutator $[A,B]:=AB-(-1)^{|A|%
\cdot|B|}BA$. Set $U^*:=\Hom_\C(U,\C^{1|0})$. The map $$\label{U'U*}
U^{\prime}\otimes 