Factorization of Graded Traces on Nichols Algebras

We study the factorization of the Hilbert series and more general graded traces of a Nichols algebra into cyclotomic polynomials. Nichols algebras play the role of Borel subalgebras of finite-dimensional quantum groups, so this observation can be viewed as an analog to the factorization of the order of finite Lie groups into cyclotomic polynomials. We prove results on this factorization and give a table of many examples of rank 1 over nonabelian groups.