Solutions of the braid equation attached to power series

Abstract

Let K be an algebraically closed characteristic 0 field and let V be the K-vector space with basis {x0,x1,x2,…}. In this paper we use the theory developed in [Citation17] to associate with each power series f∈K[[X]] satisfying f(0)=1, an involutive solution s(f):V⊗V→V⊗V, of the braid equation, and we begin the study of this correspondence. For n≥2, let Vn be the subspace of V generated by {x0,…,xn−1}. Each one of the solution s(f) induces by restriction a solution sn(f) on Vn⊗Vn. We also begin the study of these solutions.