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A note on Clifford algebras and central division algebras with involution

Published online by Cambridge University Press:  18 May 2009

D. W. Lewis
D. W. Lewis
Affiliation:
Department of Mathematics, University College, Belfif, Dublin 4Ireland
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In this note we consider the question as to which central division algebras occur as the Clifford algebra of a quadratic form over a field. Non-commutative ones other than quaternion division algebras can occur and it is also the case that there are certain central division algebras D which, while not themselves occurring as a Clifford algebra, are such that some matrix ring over D does occur as a Clifford algebra. We also consider the further question as to which involutions on the division algebra can occur as one of two natural involutions on the Clifford algebra.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 26 , Issue 2 , July 1985 , pp. 171 - 176
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

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