Identities in twisted Brauer monoids
We show that it is co-NP-hard to check whether a given semigroup identity holds in the twisted Brauer monoid $\mathcal{B}^τ_n$ with $n\ge5$.
math.GR↗
arXiv subjects
N. V. Kitov
Publications and source records attributed to N. V. Kitov.
Identities of the Kauffman Monoid $\mathcal{K}_3$
We give a transparent combinatorial characterization of the identities satisfied by the Kauffman monoid $\mathcal{K}_3$. Our characterization leads to a polynomial time algorithm to check whether a given identity holds in $\mathcal{K}_3$.
math.GR↗
Identities of the Kauffman Monoid $\mathcal{K}_4$ and of the Jones monoid $\mathcal{J}_4$
Kauffman monoids $\mathcal{K}_n$ and Jones monoids $\mathcal{J}_n$, $n=2,3,\dots$, are two families of monoids relevant in knot theory. We prove a somewhat counterintuitive result that the Kauffman monoids $\mathcal{K}_3$ and $\mathcal{K}_4$ satisfy exactly the same identities. This leads to a polynomial time algorithm to check whether a given identity holds in $\mathcal{K}_4$. As a byproduct, we also find a polynomial time algorithm for checking identities in the Jones monoid $\mathcal{J}_4$.
math.GR↗