Kei modules and unoriented link invariants

Mike Grier; Sam Nelson

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arXiv · 1102.4366

Kei modules and unoriented link invariants

Mike Grier·Sam Nelson

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Abstract

We define invariants of unoriented knots and links by enhancing the integral kei counting invariant Phi_X^Z (K) for a finite kei X using representations of the kei algebra, Z_K[X], a quotient of the quandle algebra Z[X] defined by Andruskiewitsch and Grana. 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 Z_3 which is not a Z_K[X]-module to detect the non-invertibility of a virtual knot.

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BibTeX RIS

Mike Grier, Sam Nelson. 2011-02-21. Kei modules and unoriented link invariants. https://arxiv.org/abs/1102.4366

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