  We extend T. Prosen's construction of quasilocal conserved quantities for the
XXZ model [Phys. Rev. Lett. 106, 217206 (2011)] to the case of periodic
boundary conditions. These quasilocal operators stem from a two-parameter
transfer matrix which employs a highest-weight representation of the quantum
group algebra inherent in the Yang-Baxter algebra. In contrast with the open
chain, where the conservation law is weakly violated by boundary terms, the
quasilocal operators in the periodic chain exactly commute with the Hamiltonian
and other local conserved quantities.
