Factorization of Graded Traces on Nichols Algebras
AbstractA 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 continues to hold for the graded character of the involved group and for automorphisms. First, we discuss thoroughly the diagonal case. Then, we prove factorization for a large class of nondiagonal Nichols algebras obtained by the folding construction. We conclude empirically by listing all remaining examples, which were in size accessible to the computer algebra system GAP and find that again all graded characters factorize. View Full-Text
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Lentner, S.; Lochmann, A. Factorization of Graded Traces on Nichols Algebras. Axioms 2017, 6, 32.
Lentner S, Lochmann A. Factorization of Graded Traces on Nichols Algebras. Axioms. 2017; 6(4):32.Chicago/Turabian Style
Lentner, Simon; Lochmann, Andreas. 2017. "Factorization of Graded Traces on Nichols Algebras." Axioms 6, no. 4: 32.
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