ABSTRACT
II : H ® A -----+ A, lI(h ® a) = h . a. By the adjunction property of the tensor product, we have the bijective natural correspondence
Hom(H®A,A)"":::'" Hom(A, Hom(H, A)). If we denote by 'Ij; : A -----+ H om(H, A) the map corresponding to II by the above bijection, we have the following Proposition 6.1.2 A is an H -module algebra if and only if'lj; is a morphism of algebras (Hom(H, A) is an algebra with convolution: (f *g)(h) = L f(hdg(h 2 )).
