C. Pinzari, CONJUGATION IN REPRESENTATION CATEGORIES OF MULTIPLICATIVE UNITARIES AND THEIR ACTIONS ON C-ASTERISK-ALGEBRAS, Journal of functional analysis, 135(2), 1996, pp. 390-420
A conjugation functor f on a full subcategory of R(V), the representat
ion category of a multiplicative unitary V, is defined. If V has a con
jugate, it is also regular and the domain of f is all R( V). Examples
of selfconjugate multiplicative unitaries are discussed. A coaction of
the Hopf C-algebra associated with V on the Cuntz algebra O-d is can
onically defined by a unitary object W of R(V) acting on a n-dimension
al Hilbert space. As in the group action case if d = infinity and W be
longs to the domain of f, ergodic coactions are often characterized by
the absence of finite dimensional subreprzsentations of W. Furthermor
e model actions of compact quantum group duals on C-algebras are defi
ned. (C) 1996 Academic Press, Inc.