Identities of the Kauffman Monoid $$\mathcal {K}_4$$ and of the Jones Monoid $$\mathcal {J}_4$$

Identities of the Kauffman monoid K3

“…Obviously, the next natural step in studying identities of Kauffman monoids is to characterize the identities of K n for n > 3. Recently, two of the present authors (see [Kitov and Volkov, 2019]) have found a description of the identities of K 4 . It turns out that K 4 satisfies precisely the same identities K 3 , which is a sort of surprise.…”

Identities of the Jones Monoid $\mathcal{J}_5$

“…In [9], the authors characterize the identities of J 4 . They show that for words w and v of X * , the monoid J 4 satisfies the identity w = v if c(w) = c(v) and for every non empty subset Y of c(w), Conditions (1), ( 2) and (3) of Theorem 4.6 hold.…”

“…Chen et al in [5], provide an algorithm for checking identities in K 3 . Kitov and Volkov in [9], extend this algorithm to the Kauffman monoid K 4 and also find a polynomial time algorithm for checking identities in the Jones monoid J 4 . They prove that the Kauffman monoids K 3 and K 4 satisfy exactly the same identities.…”

Representations and identities of Baxter monoids with involution

“…For a finite semigroup S, the identity checking problem Check-Id(S) is always decidable but this is not necessarily true for an infinite semigroup [46]. Studying the computational complexity of identity checking in semigroups was proposed by Sapir [31,Problem 2.4], and up to now, there are many results in this study [6,10,16,29,33].…”