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Deformations of the Witt, Virasoro, and Current Algebra

In: Generalized Lie Theory in Mathematics, Physics and Beyond

Author

Listed:
  • M. Schlichenmaier

    (University of Luxembourg, Campus Limpertsberg, 162 A, Institute of Mathematics)

Abstract

For finite-dimensional Lie algebras there is a tight connection between cohomology theory and deformations of the Lie algebra. This is not the case anymore if the Lie algebra to be deformed is infinite dimensional. Such Lie algebras might be formally rigid but nevertheless allow deformations which are even locally non-trivial. In joint work with Alice Fialowski the author constructed such geometric families for the formally rigid Witt algebra and current Lie algebras. These families are genus one (i.e. elliptic) Lie algebras of Krichever—type. In this contribution the results are reviewed. The families of algebras are given in explicit form. The constructions are induced by the geometric process of degenerating the elliptic curves to singular cubics.

Suggested Citation

  • M. Schlichenmaier, 2009. "Deformations of the Witt, Virasoro, and Current Algebra," Springer Books, in: Sergei Silvestrov & Eugen Paal & Viktor Abramov & Alexander Stolin (ed.), Generalized Lie Theory in Mathematics, Physics and Beyond, chapter 19, pages 219-234, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-85332-9_19
    DOI: 10.1007/978-3-540-85332-9_19
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