Spin groups over a commutative ring and the associated root data (Q1396721)

Usual constructions of spin and Clifford groups, restricted to the case where the basic quadratic space is hyperbolic, are examined as those of group schemes over a commutative ring. Not surprisingly they yield indeed smooth and reductive group schemes, but the proof involes a lot of calculation and uses a connection with Jordan pairs. Maximal tori and their associated root data are also constructed explicitly.