B. Williams

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20242026

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math.RA2024

Counterexamples in Involutions of Azumaya Algebras

Uriya First, Ben Williams

Suppose $A$ is an Azumaya algebra over a ring $R$ and $σ$ is an involution of $A$ extending an order- $2$ automorphism $λ : R \to R$ . We say $σ$ is extraordinary if there does not exis…

math.GR2024

Linear and smooth oriented equivalence of orthogonal representations of finite groups

Luis Eduardo García-Hernández, Ben Williams

Let $n \leq 5$ be an integer, and let $Γ$ be a finite group. We prove that if $ρ, ρ^{'} : Γ \to O (n)$ are two representations that are conjugate by an orientation-preserving diffeomorphis…