When two-dimensional Anti-de Sitter space (AdS(2)) is endowed with a non-co
nstant dilaton the origin of the central charge in the Virasoro algebra gen
erating the asymptotic symmetries of AdS(2) can be traced back to the break
ing of the SL(2,R) isometry group of AdS(2). We use this fact to clarify so
me controversial results appeared in the literature about the value of the
central charge in these models. (C) 2000 Elsevier Science B.V. All rights r
eserved.