Multivariable knot polynomials from braided Hopf algebras with automorphisms

Garoufalidis, Stavros, Rinat, Kashaev

Published 2023-11-20Version 1

We construct knot invariants from solutions to the Yang--Baxter equation associated to appropriately generalized left/right Yetter--Drinfel'd modules over a braided Hopf algebra with an automorphism. When applied to Nichols algebras, our method reproduces known knot polynomials and naturally produces multivariable polynomial invariants of knots. We discuss in detail Nichols algebras of rank $1$ and an example of rank $2$. In the latter case, we compute the associated invariants for selected knots and pose some questions about their structure.