.496> t (b) = N(g) it b; t 2 R; b 2 B g : (1:1) We shall also assume that N is a group homomorphism from G to the multiplicative group R + of positive reals (this is in fact necessarily the case if B g B h 6= f0g for all g and h). Obviously oe is determined by N . However under the present hypothesis it is not clear whether there exists a one-parameter group oe satisfying 1.1 for each group homomorphism N : G ! R + . This existence question will be dealt with when we discuss the case of crossed-products by partial actions below. Nevertheless, even