N. Takahashi (Hiroshima)

Title: Modules on quandle spaces and representations of LY algebras

Abstract: We consider quandles with geometric structures,
which are called topological quandles, smooth quandles and quandle varieties
in the topological, smooth and algebraic cases, respectively.
Certain kind of smooth quandles, called regular s-manifolds,
have been known to be related to the so-called Lie-Yamaguti algebras.

A definition of modules on topological quandles
was given by Elhamdadi-Moutou, and it generalizes to other categories.
I will explain how modules on regular s-manifolds are related to
representations of Lie-Yamaguti algebras.