# FRT construction in the case of super algebras

I'm looking on papers which are talking about the super quantum algebra osp(2|1). I want to understand how one applies the FRT construction in the case of osp(2|1). Of course there is a super permutation $P$, but if I'm right, taking a matrix $T$ whose entries represent the generators of an algebra of functions $A$ on a formal super-group and the universal $R$-matrix of the quantum superalgebra osp(2|1) and writing down the equation $$PR(T\otimes T)=(T\otimes T)PR,$$ I should find the relations defining $A$. Now, looking what happens when the quantum parameter $q$ of $R$ goes to $1$, I should find the commutation relations between the entries of a matrix in $OSp(2|1)$, but it is not so. So my question is : are there other sign contributions in the equation$$PR(T\otimes T)=(T\otimes T)PR$$ as those coming from $P$ ?

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May be just guess something like this : be careful with notation ToT-- may be you should think it leaving in algebra o supermatrices o supermatrices. Hence sign might appear from usual way. : AoB*CoD=(-1)^sgn(BC)ACoBD. Ill try to think laater – Alexander Chervov Nov 30 '12 at 16:35
I think you're right Alexander. The matrix element of the tensor product of even matrices $\left\{ F_{ij}\right\}$ and $\left\{ G_{kl}\right\}$ has the form $$(F\otimes G)_{ik,jl}=(−1)^{p(k)(p(i)+p(j))}F_{ij}G_{kl}.$$ – kieffer Dec 1 '12 at 11:34