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hal-00150494, version 1

Multivariable link invariants arising from sl(2|1) and the Alexander polynomial

Nathan Geer, Bertrand Patureau-Mirand 1

Journal of Pure and Applied Algebra 210 (2006) Journal of Pure and Applied Algebra, Volume 210, Issue 1, July 2007, Pages 283-298

Résumé : In this paper we construct a multivariable link invariant arising from the quantum group associated to the special linear Lie superalgebra sl(2|1). The usual quantum group invariant of links associated to (generic) representations of sl(2|1) is trivial. However, we modify this construction and define a nontrivial link invariant. This new invariant can be thought of as a multivariable version of the Links-Gould invariant. We also show that after a variable reduction our invariant specializes to the Conway potential function, which is a version of the multivariable Alexander polynomial.

  • 1 :  Laboratoire de Mathématiques et Applications des Mathématiques, EA 3885 (LMAM)
  • Université de Bretagne Sud
  • Domaine : Mathématiques/Topologie géométrique
    Mathématiques/Algèbres quantiques
  • Commentaire : 19 pages. (see math.GT/0609034 for other Lie superalgebras)
 
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  • Contributeur : Bertrand Patureau-Mirand <>
  • Soumis le : Mercredi 30 Mai 2007, 16:25:24
  • Dernière modification le : Mercredi 30 Mai 2007, 16:25:24