Geodesic
The Use of Hopf Algebras in the Lie Theory of Loops Related to Reductive Homogeneous Spaces
José M. Pérez-Izquierdo1
1Dpto. Matemáticas y Computación, Universidad de La Rioja, 26006 Logrono, Spain
Journal of Lie Theory, Tome 28 (2018) no. 3, pp. 781-804

Voir la notice de l'article provenant de la source Heldermann Verlag

In his generalization of reductive homogeneous spaces, Lev Sabinin introduced hyporeductive and pseudoreductive local loops. Sabinin proved that these loops admit a satisfactory Lie theoretical approach. In this paper we derive Sabinin's results in an algebraic context by means of nonassociative Hopf algebras that encode the information about the nonassociative products of these local loops.
Classification : 20N05, 17D99
Mots-clés : Non-associative Hopf algebras, Sabinin algebras, loops, hyporeductive, pseudoreductive

José M. Pérez-Izquierdo  1

1 Dpto. Matemáticas y Computación, Universidad de La Rioja, 26006 Logrono, Spain 
José M. Pérez-Izquierdo. The Use of Hopf Algebras in the Lie Theory of Loops Related to Reductive Homogeneous Spaces. Journal of Lie Theory, Tome 28 (2018) no. 3, pp. 781-804. http://geodesic.mathdoc.fr/item/JOLT_2018_28_3_a10/
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     author = {Jos\'e M. P\'erez-Izquierdo},
     title = {The {Use} of {Hopf} {Algebras} in the {Lie} {Theory} of {Loops} {Related} to {Reductive} {Homogeneous} {Spaces}},
     journal = {Journal of Lie Theory},
     pages = {781--804},
     year = {2018},
     volume = {28},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2018_28_3_a10/}
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