Cylinder braiding for quantum linear groups
If \(V\) is a module over a commutative ring, a four braid pair on \(V\) is a pair \((X,F)\) consisting of a Yang-Baxter operator \(X:V\otimes V\rightarrow V\otimes V\) and an automorphism \(F:V\rightarrow V\) such that \(X(F\otimes I)X(F\otimes I)= (F\otimes I)X(F\otimes I)X\). A four braid pair induces a representation of the braid group \(ZB_k\) associated to the Coxeter graph \(B_k\). The author constructs a certain four braid pair and studies the cylinder form induced by this four braid pair.
scientific article; zbMATH DE number 1384884