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Journal of Lie Theory 28 (2018), No. 3, 781--804
Copyright Heldermann Verlag 2018

The Use of Hopf Algebras in the Lie Theory of Loops Related to Reductive Homogeneous Spaces

José M. Pérez-Izquierdo
Dpto. Matemáticas y Computación, Universidad de La Rioja, 26006 Logrono, Spain

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.

Keywords: Non-associative Hopf algebras, Sabinin algebras, loops, hyporeductive, pseudoreductive.

MSC: 20N05, 17D99

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