Picard groups and strongly graded coalgebras

In this paper we study strongly graded coalgebras and its relation to the P icard group. A classification theorem for this kind of coalgebras is given via the second Doi's cohomology group. The strong Picard group of a coalgeb ra. is introduced in order to characterize those graded coalgebras with str ongly graded dual ring. Finally, for a Hopf algebra H we also characterize the H*-Galois coextensions with dual H-Galois extension solving the questio n proposed in Dascalescu et al., J. Algebra 178 (1995) 400-413. (C) 2001 El sevier Science B.V. All rights reserved.