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Factorization of Graded Traces on Nichols Algebras
A ubiquitous observation for finite-dimensional Nichols algebras is that as a graded algebra the Hilbert series factorizes into cyclotomic polynomials. For Nichols algebras of diagonal type (e.g., Borel parts of quantum groups), this is a consequence of the existence of a root system and a Poincare-Birkhoff-Witt (PBW) basis basis, but, for nondiagonal examples (e.g., Fomin-Kirillov algebras), this is an ongoing surprise. In this article, we discuss this phenomenon and observe that it continuesdoi:10.3390/axioms6040032 fatcat:zfn5zbusvrh2zga3insljpzcqq