Nichols algebras over finite classical groups and their deformations

• Applicant: Professor Dr. István Heckenberger
• Subject Area: Mathematics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 567878626

We use deformation and permutation group techniques to understand the structure of finite-dimensional Nichols algebras over classical groups. Specifically, we study conjugacy classes of finite classical groups that have only trivial indecomposable proper subracks. In our context, deformations of Nichols algebras arise from Hopf algebra filtrations and associated graded objects and are related to Lie theoretic structures in modular representation theory. The connection to number theory (more specifically, arithmetic geometry) arises from the study of Nichols algebras over rings and their degenerations at specific points of the spectrum of the ring.

• DFG Programme: Research Grants
• International Connection: Belgium
• Cooperation Partner: Professor Dr. Leandro Vendramin