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Post Closed as "Not suitable for this site" by Johannes Hahn, abx, Alex Degtyarev, Suvrit, Stefan Kohl♦
replaced tag 'representation'; cleaned up statement of question (I hope I did not change the intended meaning)
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Ricardo Andrade
Ricardo Andrade
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Representation Representing quaternions as matrices

char F≠2, aAssume F is a field of characteristic different than 2. Let a,b invertable from b be invertible elements in F, A and let A(a,b) -be the generalised quaternions. Using the Artin–Wedderburn theorem, there is a representation of themA(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?

Representation quaternions as matrices

char F≠2, a,b invertable from F, A(a,b) - generalised quaternions. Using Artin–Wedderburn theorem there is a representation of them over F. I found representation as Q8 but it's not over F. So, how to find representation as matrices over F?

Representing quaternions as matrices

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?

deleted 1 characters in body
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Qfwfq
Qfwfq
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char F!=2F≠2, a,b invertable from F, A(a,b) - generalised quaternions. Using Artin–Wedderburn theorem there is a representation of them over F. I found representation as Q8 but it's not over F. So, how to find representation as matrices over F?

char F!=2, a,b invertable from F, A(a,b) - generalised quaternions. Using Artin–Wedderburn theorem there is a representation of them over F. I found representation as Q8 but it's not over F. So, how to find representation as matrices over F?

char F≠2, a,b invertable from F, A(a,b) - generalised quaternions. Using Artin–Wedderburn theorem there is a representation of them over F. I found representation as Q8 but it's not over F. So, how to find representation as matrices over F?

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Andrew
Andrew
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Representation quaternions as matrices

char F!=2, a,b invertable from F, A(a,b) - generalised quaternions. Using Artin–Wedderburn theorem there is a representation of them over F. I found representation as Q8 but it's not over F. So, how to find representation as matrices over F?