Assume F is a field of characteristic different than 2. Let a, b be invertible elements in F, and let A(a,b) be the generalised quaternions. Using the Artin–Wedderburn theorem, there is a representation of A(a,b) over F. I found a representation as Q8 but it's not over F. So, how to find a representation as matrices over F?
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replaced tag 'representation'; cleaned up statement of question (I hope I did not change the intended meaning)
Ricardo Andrade
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Representing quaternions as matrices
Andrew
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