Left coideal subalgebras of Nichols algebras

尼科尔斯代数的左余理想子代数

• 批准号: 439450181
• 负责人: Professor Dr. István Heckenberger
• 金额: --
• 依托单位: Arbeitsgruppe Algebraische Lie-Theorie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/439450181?language=en
• 关键词: Left; coideal; subalgebras; Nichols; algebras

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.

Hopf代数在高对称性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，我们也很好地理解了Nichols代数的某些类型及其与李理论的相互关系，而这种理解来自于对某些类型的上理想子代数的理解。为了进一步了解Nichols代数类，以及20年前对称群上的一些已知例子，本文研究了新的非平凡左余理想子代数类。预计这种方法会产生新的基本信息，其中包括Nichols代数的维度。在这个项目中，还应该确定Nichols代数的左上理想子代数的集合的基数和这样一个集合上的偏序集结构。