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In two earlier articles we constructed algebraic-geometric families of genusone (i.e. elliptic) Lie algebras of Krichever-Novikov type. The consideredalgebras are vector fields, current and affine Lie algebras. These familiesdeform the Witt algebra, the Virasoro algebra, the classical current, and theaffine Kac-Moody Lie algebras respectively. The constructed families are notequivalent (not even locally) to the trivial families, despite the fact thatthe classical algebras are formally rigid. This effect is due to the fact thatthe algebras are infinite dimensional. In this article the results are reviewedand developed further. The constructions are induced by the geometric processof degenerating the elliptic curves to singular cubics. The algebras are ofrelevance in the global operator approach to the Wess-Zumino-Witten-Novikovmodels appearing in the quantization of Conformal Field Theory.Comment: 17 page

Global Geometric Deformations of the Virasoro Algebra, Current and Affine Algebras by Krichever–Novikov Type Algebras