  We give a review and some new relations on the structure of the monodromy
algebra (also called loop algebra) associated with a quasitriangular Hopf
algebra H. It is shown that as an algebra it coincides with the so-called
braided group constructed by S. Majid on the dual of H. Gauge transformations
act on monodromy algebras via the coadjoint action. Applying a result of Majid,
the resulting crossed product is isomorphic to the Drinfeld double D(H). Hence,
under the so-called factorizability condition given by N. Reshetikhin and M.
Semenov-Tian- Shansky, both algebras are isomorphic to the algbraic tensor
product H\otimes H. It is indicated that in this way the results of Alekseev et
al. on lattice current algebras are consistent with the theory of more general
Hopf spin chains given by K. Szlach\'anyi and the author. In the Appendix the
multi-loop algebras L_m of Alekseev and Schomerus [AS] are identified with
braided tensor products of monodromy algebras in the sense of Majid, which
leads to an explanation of the ``bosonization formula'' of [AS] representing
L_m as H\otimes\dots\otimes H.
