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Submission: 2000, Jun 09
The n-th exterior power of a central simple algebra of degree 2n is endowed with an involution which provides an interesting invariant of the algebra. In the case where the algebra decomposes as a tensor product of a subalgebra and a quaternion algebra, we describe the involution quite explicitly in terms of the corresponding involution of the subalgebra and the norm form of the quaternion algebra.
1991 Mathematics Subject Classification: 11E81, 16K20
Keywords and Phrases: Trace forms, involutions, central simple algebras
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