qa.quantum algebra - Does some version of U_q(gl(1|1)) have a basis like Lusztig's basis for dot{U(sl_2)}?

There's a non-unital algebra $dot{U}$ formed from $U_q (sl_2)$ by including a system of mutually orthogonal idempotents $1_n$, indexed by the weight lattice. You can think of this as a category with objects $mathbb{Z}$ if you prefer.

Lusztig's basis $mathbb{dot{B}}$ for $dot{U}$ has nice positivity properties: structure coefficients are in $mathbb{Z}[q,q^{-1}]$.

Has anyone tried to write down a similar type of basis for the algebra associated to $U_q (gl_{1|1})$?