Left coideal subalgebras of Nichols algebras

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Hopf algebras play an important role in the theory of non-commutative algebras with high symmetry. Further, for the structure theory of Hopf algebras, Nichols algebras are of enormous importance. In the meanwhile one understands some classes of Nichols algebras and their interrelation with Lie theory quite well, and this understanding comes from the understanding of some types of coideal subalgebras. In order to understand further classes of Nichols algebras, among others some known examples over symmetric groups from 20 years ago, it is intended to study new non-trivial classes of left coideal subalgebras. It is expected that this approach leads to new fundamental information, among others the dimension of the Nichols algebra. During the project, also the cardinality of the set of left coideal subalgebras of a Nichols algebra and the poset structure on such a set should be determined.