Orbifoldizing Hopf- and Nichols-Algebras

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

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)
• 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
• Signature of the printed copy: 0001/UMC 21036