CONSTRUCTION OF COMMUTATOR BLUEPRINTS

Abstract Commutator blueprints can be seen as blueprints for constructing RGD systems over $\mathbb {F}_2$ with prescribed commutation relations. In this paper, we construct several families of Weyl-invariant commutator blueprints, mostly of universal type. Also applying another result of the author, we obtain new examples of exotic RGD systems of universal type over $\mathbb {F}_2$ . In particular, we generalize Tits’ construction of uncountably many trivalent Moufang twin trees to higher rank, we obtain an example of an RGD system of rank $3$ such that the nilpotency degree of the groups $U_w$ is unbounded, and we construct a commutator blueprint of type $(4, 4, 4)$ that is used to answer a question of Tits from the late $1980$ s about twin buildings.