Bulletin of the london mathematical society vol:25 pages:209-230
If A is a Hopf *-algebra, the dual space A' is again a *-algebra. There is a natural subalgebra A0 of A' that is again a Hopf *-algebra. In many interesting examples, A0 will be large enough (to separate points of A). More generally, one can consider a pair (A, B) of Hopf *-algebras and a bilinear form on A x B with conditions such that, if the pairing is non-degenerate, one algebra can be considered as a subalgebra of the dual of the other.