Lentner, Simon (2012): Orbifoldizing Hopf- and Nichols-Algebras. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics |

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**DOI**: 10.5282/edoc.15363

### Abstract

The main goal of this thesis is to explore a new general construction of orbifoldizing Hopf- and Nicholsalgebras, describe the growth of the automorphism group and compare the behaviour of certain associated categories to Kirillov's orbifoldizing. Together with outlooks towards vertex algebras these aspects form the 5-fold subdivision of this thesis. The main applications of this theory is the construction of new finite-dimensional Nichols algebras with sometimes large rank. In the process, the associated group is centrally extended and the root system is folded, as shown e.g. for E6->F4 on the title page. Thus, in some sense, orbifoldizing constructs new finite-dimensional quantum groups with nonabelian Cartan-algebra.

Item Type: | Theses (Dissertation, LMU Munich) |
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Keywords: | Nichols-Algebra, Hopf-Algebra, nonabelian, orbifold |

Subjects: | 500 Natural sciences and mathematics 500 Natural sciences and mathematics > 510 Mathematics |

Faculties: | Faculty of Mathematics, Computer Science and Statistics |

Language: | English |

Date of oral examination: | 21. December 2012 |

1. Referee: | Schottenloher, Martin |

MD5 Checksum of the PDF-file: | 4bace945dd4a13e1842afa1648fc7c83 |

Signature of the printed copy: | 0001/UMC 21036 |

ID Code: | 15363 |

Deposited On: | 08. Mar 2013 07:23 |

Last Modified: | 24. Oct 2020 01:28 |