Root Graded Groups

• Applicant: Professor Dr. Bernhard Mühlherr
• Subject Area: Mathematics
• Term: since 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 428606039

The goal of the project "Root Graded Groups" is to obtain classification results for root gradings of groups. There are two main directions envisaged in the project. The first goal is to classifify the stable root gradings of groups of rank 2 that satisfy a suitable sharpness conditions. This is pursued in collaboration with Weiss (Tufts University, Medford, USA) and it can be seen as large generalization of the classification of Moufang polygons due to Tits and Weiss. The second goal is the classification of all irreducible root gradings of groups of rank at least 3. This project is pusued by Torben Wiedemann who is employed on the PhD-position of the project. Due to the rank assumption, several complications encountered in the rank 2 case are avoided. However, the ambition is to provide a classification without any additional assumption like sharpness or stability. There has been substantial progress since the start of the project in October 2019. In order to accomplish both classification projects there remains some work to do. For type BC there are still some questions to be answered in the uniqueness part. Moreover, an expicit construction of C_3-gradings over rings with nuclear involution has to be given. We are confident that we can settle these open problems within the period for which we ask for funding.

• DFG Programme: Research Grants