On Deformations and Contractions of Lie Algebras
作者: Alice FialowskiMarc de Montigny
刊名: Symmetry, Integrability and Geometry: Methods and Applications, 2006, Vol.2 , pp.048
来源数据库: Directory of Open Access Journals
关键词: Lie algebrasdeformationscontractionsKac-Moody algebras
原始语种摘要: In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras. We first discuss low-dimensional Lie algebras and illustrate thereby that whereas for every contraction there exists a reverse deformation, the converse is not true in general. Also we note that some Lie algebras belonging to parameterized families are singled out by the irreversibility of deformations and contractions. After reminding that global deformations of the Witt, Virasoro, and affine Kac-Moody algebras allow one to retrieve Lie algebras of Krichever-Novikov type, we contract the latter to find new infinite dimensional Lie algebras.
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  • mutually 互相
  • discuss 议论
  • general 普遍的
  • affine 仿射的
  • thereby 由此
  • dimensional 量纲的
  • global 球状的
  • converse 谈话
  • presentation 提示
  • opposite 对生的