Symmetry classifications of various types of exotic
quantum matter have recently become a topic of some interest, largely due to
the discovery of topological insulators.
In the context of spin liquids the question is not a new one --- Wen's
projective symmetry group is a well known approach --- but given recent
experimental and numerical interest it seems worth revisiting. I will describe work done with M. Hermele
that gives a symmetry classification of states with Z2 topological order, or in
other words, gapped Z2 spin liquids.
As the title suggests, we focus on the ways that
fractional excitations can transform under symmetry.