ABSTRACT

Definition 5.1.1 A map T E H* is called a left integral of the bialgebra H if h*T = h*(l)T for any h* E H*. The set of left integrals of H is denoted by J;. Left integrals of Heop are called right integrals for H, and their set is denoted by Ir' I Remark 5.1.2 It is clear that T E H* is a left integral if and only if L:T(X2)Xl = T(x)l 'ix E H, and it is a right integral if and only if L: T(Xl)X2 = T(x)l 'ix E H. I

We discuss briefly the name given to the above notion. Let G be a compact group. A Haar integral on G is a linear functional), on the space of continuous functions from G to R, which is translation invariant, Le.