Commutators from a hyperplane of matrices

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Clement de Seguins Pazzis


Denote by Mn(K) the algebra of n by n matrices with entries in the field K. A theorem of Albert and Muckenhoupt states that every trace zero matrix of Mn(K) can be expressed as AB − BA for some pair (A, B) ∈ Mn(K)2 . Assuming that n > 2 and that K has more than 3 elements, it is proved that the matrices A and B can be required to belong to an arbitrary given hyperplane of Mn(K).

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