  We consider various aspects of Kitaev's toric code model on a plane in the
C^*-algebraic approach to quantum spin systems on a lattice. In particular, we
show that elementary excitations of the ground state can be described by
localized endomorphisms of the observable algebra. The structure of these
endomorphisms is analyzed in the spirit of the Doplicher-Haag-Roberts program
(specifically, through its generalization to infinite regions as considered by
Buchholz and Fredenhagen). Most notably, the statistics of excitations can be
calculated in this way. The excitations can equivalently be described by the
representation theory of D(Z_2), i.e., Drinfel'd's quantum double of the group
algebra of Z_2.
