New large-rank nichols algebras over nonabelian groups with commutator subgroup Z2

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Autor/in:
Erscheinungsjahr:
2014
Medientyp:
Text
Schlagworte:
  • Covering
  • Finite-dimensional
  • Folding
  • Nichols algebra
  • Covering
  • Finite-dimensional
  • Folding
  • Nichols algebra
Beschreibung:
  • In this article, we explicitly construct new finite-dimensional, indecomposable Nichols algebras with Dynkin diagrams of type A n, C n, D n, E6,7,8, F4 over any group G of order 2ℓ with commutator subgroup isomorphic to Z2. 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 Montgomery in 1995 [22,4].Our construction uses the new notion of a covering Nichols algebra as a special case of a covering Hopf algebra [18] and produces non-faithful Nichols algebras. We give faithful examples of Doi twists for type A3, C3, D4, C4, F4 over several nonabelian groups of order 16 and 32. These are hence the first known examples of nondiagonal, finite-dimensional, indecomposable Nichols algebras of rank >2 over nonabelian groups. © 2014 Elsevier Inc.
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  • info:eu-repo/semantics/openAccess
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Forschungsinformationssystem der UHH
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oai:www.edit.fis.uni-hamburg.de:publications/f8387c98-ffa2-4420-80ee-eb1b3fd11cac