  For an arbitrary calibrated Frobenius manifold, we construct an infinite
dimensional Lie algebra, called the Virasoro-like algebra, which is a
deformation of the Virasoro algebra of the Frobenius manifold. By using the
Virasoro-like algebra we give a family of quadratic PDEs that are satisfied by
the genus-zero free energy of the Frobenius manifold. We also derive, under the
semisimplicity assumption, the Virasoro constraints for the corresponding
abstract Hodge partition function.
