In a simple algebra A over a field F with sufficient cardinality, the maximum dimension of an F-affine subspace contained in the units A^× is determined and classified via associative composition algebras and quadratic/Hermitian forms.
de Seguins Pazzis, Spaces of triangularizable matrices
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Affine subspaces of units in simple algebras
In a simple algebra A over a field F with sufficient cardinality, the maximum dimension of an F-affine subspace contained in the units A^× is determined and classified via associative composition algebras and quadratic/Hermitian forms.