  Thin Lie algebras are Lie algebras over a field, graded over the positive
integers and satisfying a certain narrowness condition. In particular, all
homogeneous components have dimension one or two, and are called diamonds in
the latter case. The first diamond is the component of degree one, and the
second diamond can only occur in degrees 3, 5, q or 2q-1, where q is a power of
the characteristic of the underlying field. Here we consider several classes of
thin Lie algebras with second diamond in degree q. In particular, we identify
the Lie algebras in one of these classes with suitable loop algebras of certain
Albert-Zassenhaus Lie algebras. We also apply a deformation technique to
recover other thin Lie algebras previously produced as loop algebras of certain
graded Hamiltonian Lie algebras.
