Involutions and Trace Forms on Exterior Powers of a Central Simple Algebra

For $A$ a central simple algebra of degree $2n$, the $n$th exterior power algebra $\lambda^n A$ is endowed with an involution which provides an interesting invariant of $A$. In the case where $A$ is isomorphic to $Q \otimes B$ for some quaternion algebra $Q$, we describe this involution quite explicitly in terms of the norm form for $Q$ and the corresponding involution for $B$.

2000 Mathematics Subject Classification: 16K20 (11E81 20G05)

Keywords and Phrases: Trace forms, involutions, central simple algebras

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