Right l-groups, geometric Garside groups, and solutions of the quantum Yang–Baxter equation

Uniconnected solutions to the Yang–Baxter equation arising from self-maps of groups

“…2021/04/06 08:37 Example 1. Let G be a right ℓ-group [23], that is, a group with a lattice order, satisfying…”

“…in X 3 , these solutions found increasing attention during the past thirty years (see, e. g., [30,12,29,15,10,19,21,4,5,14,11,6,7,8,23,1,18,25,26,27,28]. Due to their close connection with braidings, they arise in various topics, including non-commutative regular rings [13,14], regular affine groups [4,2,3], Hopf-Galois theory [11,6,16,1], and Garside groups [7,8,23].…”

A right-invariant lattice-order on groups of paraunitary matrices

“…Existence and uniqueness for a factorization that is not left-contractable is shown in a more general context in [Rum15,Proposition 12].…”

Two theorems on balanced braces

“…The systematic study of set-theoretic solutions began with the papers of Gateva-Ivanova and Van den Bergh [19], Etingof et al [9], and Lu et al [25]. Due to the ubiquity of braidings, numerous connections to other mathematical fields were discovered, including Poisson Lie groups [37], Sklyanin algebras [36], noncommutative regular rings [12,13], Hopf-Galois extensions [1,5], right-symmetric Lie algebras [3,30], and Garside groups [6,7,31].…”