For a central simple algebra with an orthogonal involution (A, σ) over a field k of characteristic different from 2, we relate the multipliers of similitudes of (A, σ) with the Clifford algebra C(A, σ). We also give a complete description of the group of multipliers of similitudes when deg A ≤ 6 or when the virtual cohomological dimension of k is at most 2.
Preeti, R., & Tignol, J.-P. (2004). Multipliers of Improper Similitudes. Documenta Mathematica, 9(1), 183-204. https://hdl.handle.net/2078.5/268653 (Original work published 2004)