Multipliers of Improper Similitudes

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 $2$.

2000 Mathematics Subject Classification: 11E72.

Keywords and Phrases: Central simple algebra with involution, hermitian form, Clifford algebra, similitude.

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