Multipliers of improper similitudes

Abstract

For a central simple algebra with an orthogonal involution $(A,\sigma )$ over a field $k$ of characteristic different from 2, we relate the multipliers of similitudes of $(A,\sigma )$ with the Clifford algebra $C(A,\sigma )$. We also give a complete description of the group of multipliers of similitudes when $\mathrm{deg}A\le 6$ or when the virtual cohomological dimension of $k$ is at most 2.