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.
