The Jordan triple of any Jordan algebra gives rise to a ternary Jordan algebra. We study these ternary algebras in terms of operads. We give the description of the operad of ternary Jordan algebras as a quadratic operad and prove that the quadratic dual of this operad is the operad of partially antisymmetric, partially associative ternary algebras. Le triple de Jordan munit toute algèbre de Jordan d'une structure d'algèbre de Jordan ternaire. Nous étudions ces algèbres ternaires en termes d'opérades. Nous donnons une description de l'opérade quadratique des algèbres de Jordan ternaires et montrons que son dual quadratique est l'opérade des algèbres ternaires partiellement associatives, partiellement antisymétriques.
Publié le : 1999-05-18
Classification:
Jordan algebras,
operad,
"Jordan algebras,
Jordan triple system,
n-ary algebra,
Koszul duality,
operad",
17X, 17A30,17A40,17B60,17C05,17C10,17C45,
[MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA]
@article{hal-00129633,
author = {Gnedbaye, Allahtan Victor and Wambst, Marc},
title = {Jordan Triples and Operads.},
journal = {HAL},
volume = {1999},
number = {0},
year = {1999},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00129633}
}
Gnedbaye, Allahtan Victor; Wambst, Marc. Jordan Triples and Operads.. HAL, Tome 1999 (1999) no. 0, . http://gdmltest.u-ga.fr/item/hal-00129633/