  We consider the representations of Hopf algebras involved in some physical
models, namely, factorizable S-matrix models (FSM's), one-dimensional quantum
spin chains (QSC's) and statistical vertex models (SVM's). These physical
representations have definite hermiticity assignments and lead to star
structures on the corresponding Hopf algebras. It turns out that for FSM's and
the quantum mechanical time-evolution of QSC's the corresponding stars are
compatible with the Hopf structures. However, in the case of statistical models
the resulting star structure is not a Hopf one but what we call a twisted star.
Real representations of a twisted star Hopf algebra do not close under the
usual tensor product of representations. We briefly comment on the relation of
these results with the Wick rotation.
