Turaev group coalgebras and twisted Drinfeld double Shouhong Wang 16W30Hopf algebraHopf dual pairingTuraev group coalgebraquasitriangular Turaev group coalgebratwisted Drinfeld doubleCartan data A new method of constructing Turaev group coalgebras with quasitriangular structure is introduced. Starting from a Hopf dual pairing $(A,B,\sigma)$ with appropriate homomorphisms: $\phi:\pi\longrightarrow\Aut(A)$ and $\psi:\pi\longrightarrow\Aut(B)$, we construct a twisted Drinfeld double $D(A,B,\sigma;\phi,\psi)$ which is a Turaev $\mathscr{S}(\pi)$-coalgebra, where the group $\mathscr{S}(\pi)$ is a twisted semi-direct square of $\pi$. Moreover, when $A$ or $B$ is finite-dimensional, we define a non-trivial quasitriangular structure on $D(A,B,\sigma;\phi,\psi)$. This approach allows us to produce new examples of Turaev $\pi$-coalgebras for many infinite groups $\pi$ such as $GL_n(\mathbbm{k})$ and $(\mathbb{C}^{*})^{\ell}$ with $\ell\geq1$. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3569 10.1512/iumj.2009.58.3569 en Indiana Univ. Math. J. 58 (2009) 1395 - 1418 state-of-the-art mathematics http://iumj.org/access/