Orbifoldizing Hopf- and Nichols-Algebras

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.