Divisibility relations for the dimensions and Hilbert series of Nichols algebras of non-abelian group type
Copyright policy )Divisibility relations for the dimensions and Hilbert series of Nichols algebras of non-abelian group type
We present a divisibility relation for the dimensions and Hilbert series of certain classes of Nichols algebras of non-abelian group type, which generalizes Nichols algebras over Coxeter groups with constant cocycle -1. For this we introduce three groups of isomorphisms acting on Nichols algebras, which generalize the exchange operator introduced by Milinski and Schneider for Coxeter groups in "Pointed indecomposable Hopf algebras over Coxeter groups".
21 pages
- Philipps-University of Marburg Germany
quandles, Hopf algebras and their applications, Hilbert series, Graded rings and modules (associative rings and algebras), Yetter-Drinfeld modules, racks, Hopf algebras, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), 16T05, 16W50, Nichols algebras, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
quandles, Hopf algebras and their applications, Hilbert series, Graded rings and modules (associative rings and algebras), Yetter-Drinfeld modules, racks, Hopf algebras, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), 16T05, 16W50, Nichols algebras, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
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