Geodesic
Kei modules and unoriented link invariants
Homology, homotopy, and applications, Tome 16 (2014) no. 1, pp. 167-177.

Voir la notice de l'article provenant de la source International Press of Boston

We define invariants of unoriented knots and links by enhancing the integral kei counting invariant $\Phi_X^{\mathbb{Z}}(K)$ for a finite kei $X$ using representations of the kei algebra, $\mathbb{Z}_K[X]$, a quotient of the quandle algebra $\mathbb{Z}[X]$ defined by Andruskiewitsch and Graña. We give an example that demonstrates that the enhanced invariant is stronger than the unenhanced kei counting invariant. As an application, we use a quandle module over the Takasaki kei on $\mathbb{Z}_3$ which is not a $\mathbb{Z}_K[X]$-module to detect the non-invertibility of a virtual knot.
DOI : 10.4310/HHA.2014.v16.n1.a10
Classification : 57M25, 57M27
Keywords: Kei algebra, kei module, involutory quandle, enhancement of counting invariants 
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Michael Grier; Sam Nelson. Kei modules and unoriented link invariants. Homology, homotopy, and applications, Tome 16 (2014) no. 1, pp. 167-177. doi : 10.4310/HHA.2014.v16.n1.a10. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2014.v16.n1.a10/

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