Orbifoldizing Hopf- and Nichols-Algebras

Lentner, Simon (2012): Orbifoldizing Hopf- and Nichols-Algebras. Dissertation, LMU München: Fakultät für Mathematik, Informatik und Statistik

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.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Keywords: Nichols-Algebra, Hopf-Algebra, nonabelian, orbifold
• Themengebiete: 500 Naturwissenschaften und Mathematik ; 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Fakultäten: Fakultät für Mathematik, Informatik und Statistik
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 21. Dezember 2012
• 1. Bericht­erstatter:in: Schottenloher, Martin