Clifford orders (A17)

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

The Clifford algebra of a quadratic space over a number field is a graded semisimple algebra that determines the quadratic space up to isometry. The project investigates the arithmetic analogue, the Clifford order of a quadratic lattice over a ring of integers. On the one hand the Clifford order defines a new invariant for integral quadratic forms and on the other hand the lattices provide a new tool to study the unit groups of their Clifford orders. The relevant lattices and their automorphisms play a central role in Project A22 and the Clifford orders define interesting convex subsets in buildings, as they are studied in Project A21

• DFG Programme: CRC/Transregios
• Subproject of: TRR 195: Symbolic Tools in Mathematics and their Application
• Applicant Institution: Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau
• Project Head: Professorin Dr. Gabriele Nebe