by Markus Rost (Notes, July 2022, 19 pages)
We formulate and prove a certain relation in the automorphism group of H⊗H for an involutive Hopf algebra H (S2=1). It lifts the standard cubic relation in the automorphism group of a free group of rank 2.
More generally, the braid group B4 acts on H⊗H for any Hopf algebra H.
We pose also the question for the universal relations which hold for commutative Hopf algebras and for cocommutative Hopf algebras.
The main purpose of the current text is to require advice on the current status of the topic.
Full text (August 2, 2022): [pdf]