Affine Lie algebras and tame quivers

• I. Frenkel ^[1] ; A. Malkin ^[1] ; M. Vybornov ^[2]
  1. [1] Yale University

     Yale University

     Town of New Haven, Estados Unidos

     
  2. [2] Duke University

     Duke University

     Township of Durham, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 7, Nº. 1, 2001, págs. 1-56
• Idioma: inglés
• DOI: 10.1007/pl00001397
• Enlaces
  • Texto completo (pdf)
• Resumen

  • C.M. Ringel defined a Hall algebra associated with the category of representations of a quiver of Dynkin type and gave an explicit description of the structure constants of the corresponding Lie algebra. We utilize functorial properties of the Hall algebra to give a simple proof of the Ringel's result, and to generalize it to the case of a quiver of affine type. In particular a linear spanning set of the positive part of an affine Lie algebra and the corresponding structure constants are described in terms of quivers.