caa a22 4500 463197607 CHVBK 20180406164927.0 cr unu---uuuuu 170326e20071101xx s 000 0 eng 10.1007/s10773-007-9383-5 doi (NATIONALLICENCE)springer-10.1007/s10773-007-9383-5 Global Geometric Deformations of the Virasoro Algebra, Current and Affine Algebras by Krichever-Novikov Type Algebras [Elektronische Daten] [A. Fialowski, M. Schlichenmaier] 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. Springer Science+Business Media, LLC, 2007 Deformations of algebras nationallicence Rigidity nationallicence Wess-Zumino-Witten-Novikov models nationallicence Krichever-Novikov algebras nationallicence Conformal field theory nationallicence Fialowski A. Institute of Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary aut Schlichenmaier M. University of Luxembourg, Institute of Mathematics, Campus Limpertsberg, 162 A, Avenue de la Faiencerie, 1511, Luxembourg, Luxembourg aut International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/11(2007-11-01), 2708-2724 0020-7748 46:11<2708 2007 46 10773 https://doi.org/10.1007/s10773-007-9383-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-007-9383-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fialowski A. Institute of Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary aut NATIONALLICENCE 700 1- Schlichenmaier M. University of Luxembourg, Institute of Mathematics, Campus Limpertsberg, 162 A, Avenue de la Faiencerie, 1511, Luxembourg, Luxembourg aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/11(2007-11-01), 2708-2724 0020-7748 46:11<2708 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer