We consider an aggregation equation in $\mathbb R^d$, $d\ge 2$ with
fractional dissipation: $u_t + \nabla\cdot(u \nabla K*u)=-\nu
\Lambda^\gamma u $, where $\nu\ge 0$, $0 < \gamma\le 2$ and
$K(x)=e^{-|x|}$. In the supercritical case, $0 < \gamma < 1$, we obtain
new local wellposedness results and smoothing properties of
solutions. In the critical case, $\gamma=1$, we prove the global
wellposedness for initial data having a small $L_x^1$ norm. In the
subcritical case, $\gamma > 1$, we prove global wellposedness and
smoothing of solutions with general $L_x^1$ initial data.