Quantum Double Model and Chern-Simons with finite gauge group

Question

Is there a relationship between Kitaev's quantum double model for a finite group $ G $ and a Chern Simons theory with finite gauge group $ G $. They are apparently both related to quantum groups and hopf algebras associated with $ G $.

https://arxiv.org/abs/hep-th/9111004

Answer 1

A general Chern-Simons theory with finite group $G$ is labeled by an element $\omega$ of $H^4[G, Z]$, which for finite or compact groups is equal to $H^3[G, U(1)]$. If $\omega$ is trivial, then we just have a pure gauge theory. The Hamiltonian version of a finite group $G$ gauge theory is equivalent to Kitaev's quantum double model with group $G$, if the Gauss's law is imposed energetically instead of being a Hilbert space constraint. One can also generalize Kitaev's quantum double model to allow for the cohomology twist.