$\newcommand{\dmod}{\text{-}\mathrm{mod}}$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 $H(A)\otimes H(A)^{\mathrm{op}}$?