Gröbner techniques for PBW deformations: parametrization, representations, applications (B06)

• Subject Area: Mathematics
• Term: from 2017 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 286237555

PBW (Poincaré-Birkhoff-Witt) deformations of smash products are moduli spaces of algebra deformations with a regularity condition containing many prominent cases, such as various types of Hecke and Cherednik algebras, which are closely related to representations of algebraic groups and of finite groups. Both the parametrization of the moduli spaces, and the algebra structure and representation theory of the deformed objects pose many important open prob-lems which we will study constructively and algorithmically using Gröbner basis techniques. Further applications in-clude current algebras and algebraic systems theory.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 195: Symbolic Tools in Mathematics and their Application
• Applicant Institution: Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau
• Project Heads: Professor Dr. Ghislain Fourier, since 1/2021; Professor Dr. Ulrich Thiel, since 1/2021; Professorin Dr. Eva Zerz