Azumaya Algebras With Orthogonal Involution Admitting an Improper Isometry

Uriya A. First

Let $(A,\sigma )$ be an Azumaya algebra with orthogonal involution over a ring $R$ with $2\in R^{\times }$. We show that if $(A,\sigma )$ admits an improper isometry, i.e., an element $a\in A$ wi…