$\newcommand{\dmod}{\text{-}\mathrm{mod}}$Let $A$ be a finite-dimensional quasi-Hopf algebra over a field $k$ and $A\dmod$ be the category of finite dimensional left $A$-modules. Since $A\dmod$ is a rigid monoidal category, its Drinfel’d center $\mathcal{Z}(A\dmod)$ is a rigid braided monoidal category. So we obtain quasi triangular quasi hopf algebra $D(A)$ from $\mathcal{Z}(A\dmod)$ by using tannaka duality.

Question 1:Is there a (categorical) definition of Heisenberg double $H(A)$ for quasi hopf algebra $A$?

Question 2: If the answer to the above question is yes,is $D(A)$ a subalgebra of $H(A)\otimes H(A)^{\mathrm{op}}$?