2006/10/27 by Alice Fialowski, Martin Schlichenmaier · 22 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Affine Lie algebra #Affine transformation #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Cellular algebra #Conformal field theory #Conformal map #Current algebra #Lie algebra #Lie conformal algebra #Mathematical analysis #Mathematics #Non-associative algebra #Nonlinear Waves and Solitons #Novikov self-consistency principle #Pure mathematics #Universal enveloping algebra #Virasoro algebra #math-ph #math.MP #math.QA #msc:14D15 #msc:14H52 #msc:17B56 #msc:17B65 #msc:17B66 #msc:17B68 #msc:30F30 #msc:81T40
paper · pdf · doi:10.1007/s10773-007-9383-5
published in International Journal of Theoretical Physics 46(11), 2708-2724 (Springer Science+Business Media) · 17 pages
arxiv created 2006/10/27 · openalex publication_date 2007/05/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.