no. 17-18
Algebra/Lie Algebras
Lie n-racks
[n-casiers de Lie]

Présenté par : the Editorial Board

Biyogmam, Guy Roger1
1 Department of Mathematics, Southwestern Oklahoma State University, 100 Campus Drive, Weatherford, OK 73096, USA
Comptes Rendus. Mathématique, Tome 349 (2011) no. 17-18, pp. 957-960.

Dans cette Note, nous introduisons la catégorie des n-casiers de Lie et nous généralisons plusieurs résultats connus pour les racks. En particulier, nous montrons que lʼespace tangent dʼun n-casier de Lie en lʼélément neutre a une structure de n-algèbre de Leibniz.

In this Note, we introduce the category of Lie n-racks and generalize several results known on racks. In particular, we show that the tangent space of a Lie n-rack at the neutral element has a Leibniz n-algebra structure.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.07.019
Biyogmam, Guy Roger 1

1 Department of Mathematics, Southwestern Oklahoma State University, 100 Campus Drive, Weatherford, OK 73096, USA 
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Biyogmam, Guy Roger. Lie n-racks. Comptes Rendus. Mathématique, Tome 349 (2011) no. 17-18, pp. 957-960. doi : 10.1016/j.crma.2011.07.019. http://www.numdam.org/articles/10.1016/j.crma.2011.07.019/

[1] J. Conway, G. Wraith, Unpublished correspondence, 1958.

[2] Casas, J.M.; Loday, J.L.; Pirashvili, T. Leibniz n-algebras, Forum Math., Volume 14 (2002), pp. 189-207

[3] Grabowski, J.; Marmo, G. On Filippov algebroids and multiplicative Nambu–Poisson structures, Differential Geom. Appl., Volume 12 (2000), pp. 35-50

[4] Joyce, D. A classifying invariant of knots: the knot quandle, J. Pure Appl. Algebra, Volume 23 (1982), pp. 37-65

[5] Kinyon, K. Leibniz algebra, Lie racks and digroups, J. Lie Theory, Volume 17 (2007), pp. 99-111

[6] Loday, J.-L. Cyclic Homology, Springer-Verlag, Berlin, Heidelberg, New York, 1992

[7] Loday, J.-L. Une Version Non Commutative des Algebres de Lie : Les Algebres de Leibniz, Enseign. Math., Volume 39 (1993), pp. 269-293

[8] Takasaki, M. Abstraction of symmetric transformation, Tohoku Math. J., Volume 49 (1942/1943)

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