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arXiv · 1306.5684

New Large-Rank Nichols Algebras Over Nonabelian Groups With Commutator Subgroup Z_2

Simon D. Lentner
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Abstract

In this article, we explicitly construct new finite-dimensional, link-indecomposable Nichols algebras with Dynkin diagrams of type An,Cn,Dn,E6,E7,E8,F4 over any group G with commutator subgroup isomorphic to Z_2.The construction is generic in the sense that the type just depends on the rank and center of G, and thus positively answers for all groups of this class a question raised by Susan Montgomory in 1995 [Mont95][AS02]. Our construction uses the new notion of a covering Nichols algebra as a special case of a covering Hopf algebra [Len12] and produces non-faithful Nichols algebras. However, we give faithful examples of Doi twists for type A3,C3,D4,F4 over several nonabelian groups of order 16 and 32. These are hence the first known examples of faithful, finite-dimensional, link-indecomposable Nichols algebras of rank >2 over nonabelian groups.

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Simon D. Lentner. 2013-06-24. New Large-Rank Nichols Algebras Over Nonabelian Groups With Commutator Subgroup Z_2. https://arxiv.org/abs/1306.5684

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