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Nouvelles structures de nambu et super-théorème d'amitsur-levitzki by Gie-P

Nouvelles structures de nambu et super-théorème d'amitsur-levitzki

by Gie-P
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Book cover type: Paperback
  • ISBN13: 9786131532245
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Univ Europeenne
  • Publisher Imprint: Univ Europeenne
  • Publication Date:
  • Pages: 180
  • Original Price: GBP 49.0
  • Language: French
  • Edition: N/A
  • Item Weight: 273 grams
  • BISAC Subject(s): Algebra / General

Dans cette étude, nous cherchons à établir des identités polynomiales dans le cadre de la combinatoire non-commutative. Dans un premier temps, nous présentons de nouvelles structures de Nambu-Lie, en classifiant totalement les (n-1)-structures sur l'espace R n, et en donnant une méthode permettant de construire des crochets de tout ordre sur une algèbre de Lie. Nous proposons également une quantification de l'une de nos structures, grâce aux polynômes standards et aux algèbres de Clifford d'indice pair. Dans un second moment, en généralisant la notion de polynôme standard au cas des algèbres graduées, nous cherchons à démontrer une version du théorème d'Amitsur-Levitzki sur les superalgèbres de Lie osp(1,2n) en suivant une démonstration de Kostant dans le cas classique. Nous sommes amenés à démontrer des super-versions des propriétés et résultats nécessaires à la démonstration dans le cas classique, notamment en définissant un super-opérateur de transgression de Cartan-Chevalley.

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