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
tkhsnbys@hiroshima-u.ac.jp
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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