Geodesic
Involutions and trace forms on exterior powers of a central simple algebra
Documenta mathematica, Tome 6 (2001), pp. 97-118.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $B$.
Classification : 16K20, 11E81, 20G05
Keywords: trace forms, involutions, central simple algebras 
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     author = {Garibaldi, R.Skip and Qu\'eguiner-Mathieu, Anne and Tignol, Jean-Pierre},
     title = {Involutions and trace forms on exterior powers of a central simple algebra},
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     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2001__6__a16/}
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Garibaldi, R.Skip; Quéguiner-Mathieu, Anne; Tignol, Jean-Pierre. Involutions and trace forms on exterior powers of a central simple algebra. Documenta mathematica, Tome 6 (2001), pp. 97-118. http://geodesic.mathdoc.fr/item/DOCMA_2001__6__a16/