In these lecture notes we aim for a pedagogical introduction to both classical and quantum
integrability. Starting from Liouville integrability and passing through Lax pair and r-matrix …

Our primary focus is on the theory of skew braces, specifically exploring their connection
with combinatorial solutions to the Yang–Baxter equation. Skew braces have recently …

We consider one dimensional block cellular automata, where the local update rules are
given by Yang-Baxter maps, which are set theoretical solutions of the Yang-Baxter …

The complex coupled short‐pulse equation (ccSPE) describes the propagation of ultrashort
optical pulses in nonlinear birefringent fibers. The system admits a variety of vector soliton …

Let p be a prime number. We show that there is a one-to-one correspondence between the
set of strongly nilpotent braces and the set of nilpotent pre-Lie rings of cardinality pn, for …

Motivated by recent findings on the derivation of parametric noninvolutive solutions of the
Yang–Baxter equation, we reconstruct the underlying algebraic structures, called near …

We consider involutive, non-degenerate, finite set-theoretic solutions of the Yang–Baxter
equation (YBE). Such solutions can be always obtained using certain algebraic structures …

We examine links between the theory of braces and set-theoretical solutions of the Yang–
Baxter equation, and fundamental concepts from the theory of quantum integrable systems …

In this paper a simple algebraic formula is obtained for the correspondence between finite
right nilpotent F p-braces and finite nilpotent pre-Lie algebras. This correspondence agrees …

In 2014, Wolfgang Rump showed that there exists a correspondence between left nilpotent
right ℝ-braces and pre-Lie algebras. This correspondence, established using a geometric …