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On symplectic quandles

Esteban Adam Navas·Sam Nelson
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Abstract

We study the structure of symplectic quandles, quandles which are also R-modules equipped with an antisymmetric bilinear form. We show that every finite dimensional symplectic quandle over a finite field F or arbitrary field F of characteristic other than 2 is a disjoint union of a trivial quandle and a connected quandle. We use the module structure of a symplectic quandle over a finite ring to refine and strengthen the quandle counting invariant.

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Esteban Adam Navas, Sam Nelson. 2007-09-20. On symplectic quandles. https://arxiv.org/abs/math/0703727

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