We formulate the Hopf algebra underlying the su(2|2) worldsheet S-matrix of
the AdS_5 x S^5 string in the AdS/CFT correspondence. For this we extend the
previous construction in the su(1|2) subsector due to Janik to the full algebra
by specifying the action of the coproduct and the antipode on the remaining
generators. The nontriviality of the coproduct is determined by length-changing
effects and results in an unusual central braiding. As an application we
explicitly determine the antiparticle representation by means of the
established antipode.Comment: 12 pages, no figures, minor changes, typos corrected, comments and
references added, v3: three references adde
