Anticommutative extension of the Adler map
  We construct a noncommutative (Grassmann) extension of the well known Adler Yang-Baxter map. It satisfies the Yang-Baxter equation, it is reversible and birational. Our extension preserves all the properties of the original map except the involutivity. 
Sotiris Konstantinou-Rizos and Alexander V. Mikhailov
nlin.SI