Let 1< n. The Kauffman monoid Kn is the monoid generated by h1,...,hn-1,c, subject to the following relations:
hihj=hjhi, ∀ 1 ≤ i,j ≤ n-1, if |i-j| ≥ 2
hihjhi=hi, ∀ 1 ≤ i,j ≤ n-1, if |i-j| = 1
hi2=chi=hic, ∀ 1 ≤ i ≤ n-1.
Jones monoid Jn is the monoid generated by h1,...,hn-1, subject to the first and second relations and the relation hi2=hi, for all 1 ≤ i ≤ n-1. In [1], the authors prove that the Kauffman monoids K3 and K4 satisfy the same identities. However, by delivering an identity, they show that K4 and K5 do not satisfy the same identities. Moreover, this identity shows that J4 and J5 do not satisfy the same identities. In this talk, we will present a characterization of identities satisfied by the Jones monoid J5.[1] Kitov N. V., Volkov M. V., Identities of the Kauffman monoid K4 and of the Jones monoid J4, Fields of Logic and Computation III, Lect. Notes Comp. Sci., vol. 12180, Springer, Cham, 2020, 156-178.