Dirac Lie groups, Dirac homogeneous spaces and the theorem of Drinfeld Madeleine Jotz 53D1722E1570H45Poisson Lie groupsDirac manifoldsLie algebras The notions of \emph{Poisson Lie group} and \emph{Poisson homogeneous space} are extended to the Dirac category. The theorem of Drinfeld on the one-to-one correspondence between Poisson homogeneous spaces of a Poisson Lie group and a special class of Lagrangian subalgebras of the Lie bialgebra associated to the Poisson Lie group is proved to hold in this more general setting. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4421 10.1512/iumj.2011.60.4421 en Indiana Univ. Math. J. 60 (2011) 319 - 366 state-of-the-art mathematics http://iumj.org/access/