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arXiv · 1909.01384

On the non-neutral component of outer forms of the orthogonal group

Uriya A. First
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Abstract

Let $(A,\sigma)$ be a central simple algebra with an orthogonal involution. It is well-known that $O(A,\sigma)$ contains elements of reduced norm $-1$ if and only if the Brauer class of $A$ is trivial. We generalize this statement to Azumaya algebras with orthogonal involution over semilocal rings, and show that the "if" part fails if one allows the base ring to be arbitrary.

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Uriya A. First. 2019-09-03. On the non-neutral component of outer forms of the orthogonal group. https://doi.org/10.1016/j.jpaa.2020.106477

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