Left coideal subalgebras of Nichols algebras

Hopf代数在高度对称的非交换代数理论中占有重要地位。此外，对于Hopf代数的结构理论来说，Nichols代数是非常重要的。同时，对尼科尔斯代数的某些类别及其与李论的关系有了较好的认识，这种认识来自于对某些类型的共理想子代数的认识。为了进一步了解尼科尔斯代数的类别，以及20年前对称群上已知的一些例子，打算研究新的非平凡左共理想子代数的类别。预计这种方法将带来新的基本信息，其中包括尼科尔斯代数的维度。在项目中，还需要确定Nichols代数的左共理想子代数集合的基数以及该集合上的偏置结构。

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.