We propose a specific class of matrices that participate in factorization problems that turn out
to be equivalent to constant and entwining (non-constant) pentagon, reverse-pentagon or …

It is known that the local Yang–Baxter equation is a generator of potential solutions to
Zamolodchikov's tetrahedron equation. In this paper, we show under which additional …

In the recent years there is a growing interest in deriving and extending discrete integrable
systems to the non-abelian domain. At the same time there is an intrinsic connection of …

We construct birational maps that satisfy the parametric set-theoretical Yang–Baxter
equation and its entwining generalisation. For this purpose, we employ Darboux …

We present the explicit form of a family of Liouville integrable maps in 3 variables, the so-
called triad family of maps and we propose a multi-field generalisation of the latter. We show …

In this paper we show that there are explicit Yang–Baxter (YB) maps with Darboux–Lax
representation between Grassman extensions of algebraic varieties. Motivated by some …

In this paper, we construct a Grassmann extension of a Yang-Baxter map which first
appeared in the work of Kouloukas and Papageorgiou [J. Phys. A: Math. Theor. 42, 404012 …

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We construct novel solutions to the set-theoretical entwining Yang-Baxter equation. These
solutions are birational maps involving non-commutative dynamical variables which are …

We give an action of the symmetric group on non-commuting indeterminates in terms of
series in the corresponding Mal'cev–Newmann division ring. The action is constructed from …