Identities of the Kauffman Monoid K_4 and of the Jones monoid J_4

10/21/2019

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by   N. V. Kitov, et al.

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Kauffman monoids K_n and Jones monoids J_n, n=2,3,..., are two families of monoids relevant in knot theory. We prove a somewhat counterintuitive result that the Kauffman monoids K_3 and K_4 satisfy exactly the same identities. This leads to a polynomial time algorithm to check whether a given identity holds in K_4. As a byproduct, we also find a polynomial time algorithm for checking identities in the Jones monoid J_4.