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Journal of Lie Theory 31 (2021), No. 4, 897--932
Copyright Heldermann Verlag 2021

Modules over Geometric Quandles and Representations of Lie-Yamaguti Algebras

Nobuyoshi Takahashi
Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, Japan

We study quandle modules over geometric quandles Q, i.e., quandles endowed with geometric structures. In the case Q is a regular s-manifold, we exhibit how modules over Q are related with representations of Lie-Yamaguti algebras.

Keywords: Quandle, regular s-manifold, Lie-Yamaguti algebra, Lie triple system, representation.

MSC: 22A30; 14M17, 17D99, 22F30.

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