  In two earlier articles we constructed algebraic-geometric families of genus
one (i.e. elliptic) Lie algebras of Krichever-Novikov type. The considered
algebras are vector fields, current and affine Lie algebras. These families
deform the Witt algebra, the Virasoro algebra, the classical current, and the
affine Kac-Moody Lie algebras respectively. The constructed families are not
equivalent (not even locally) to the trivial families, despite the fact that
the classical algebras are formally rigid. This effect is due to the fact that
the algebras are infinite dimensional. In this article the results are reviewed
and developed further. The constructions are induced by the geometric process
of degenerating the elliptic curves to singular cubics. The algebras are of
relevance in the global operator approach to the Wess-Zumino-Witten-Novikov
models appearing in the quantization of Conformal Field Theory.
