Osaka Journal of Mathematics

On symplectic quandles

Esteban Adam Navas and Sam Nelson

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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 $\mathbb{F}$ or arbitrary field $\mathbb{F}$ 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.

Article information

Osaka J. Math., Volume 45, Number 4 (2008), 973-985.

First available in Project Euclid: 26 November 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 176D99 57M27: Invariants of knots and 3-manifolds 55M25: Degree, winding number


Navas, Esteban Adam; Nelson, Sam. On symplectic quandles. Osaka J. Math. 45 (2008), no. 4, 973--985.

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