Multivariable polynomials of knots from Nichols algebras

Using finite dimensional Nichols algebras with automorphisms, we construct R-matrices with entries polynomials in the structure constants of the Nichols algebras. The R-matrices satisfy the Yang-Baxter equation and can be used to define multivariable polynomials of knots that generalize the colored Jones polynomial. For a Nichols algebra of rank 2, we define a sequence of polynomials $V_n(t,q)$ in two variables, whose first knot invariant is the Links-Gould polynomial and the second one $V_2$ is a new polynomial invariant that gives bounds for the Seifert-genus of a knot. Joint work with Rinat Kashaev.