Higher conjugations and the Yang-Baxter equation (Q1851344)

In a previous paper [Commun. Algebra 29, No. 8, 3351-3363 (2001; Zbl 0999.16034)] the author constructed actions of the symmetric groups on tensor powers of commutative or cocommutative Hopf algebras. The current paper sets these actions in the wider context of representations of the braid group and solutions of the Yang-Baxter equation, a linearization of the braid relations. The author gives a full account of the relations between braid group and symmetric group actions, between actions on \(n\)-fold and \(n-1\)-fold tensor products, and of the duality present. Remark: In the proof of Proposition 1.1 \(p^1\) should be \(p'\).