## Multipliers of improper similitudes

### Summary

Summary: 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 $\deg A \leq 6$ or when the virtual cohomological dimension of $k$ is at most 2.

11E72

### Keywords/Phrases

central simple algebra with involution, Hermitian form, Clifford algebra, similitude