Involutions and trace forms on exterior powers of a central simple algebra
R.Skip Garibaldi
UCLA, Dept. of Mathematics, UMR CNRS 7539, Los Angeles, CA 90095-1555, Département de Mathématiques, USA Université Paris 13Anne Quéguiner-Mathieu
UCLA, Dept. of Mathematics, UMR CNRS 7539, Los Angeles, CA 90095-1555, Département de Mathématiques, USA Université Paris 13Jean-Pierre Tignol
Départment de Mathématiques, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
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Abstract
For a central simple algebra of degree , the th exterior power algebra is endowed with an involution which provides an interesting invariant of . In the case where is isomorphic to for some quaternion algebra , we describe this involution quite explicitly in terms of the norm form for and the corresponding involution for .
Cite this article
R.Skip Garibaldi, Anne Quéguiner-Mathieu, Jean-Pierre Tignol, Involutions and trace forms on exterior powers of a central simple algebra. Doc. Math. 6 (2001), pp. 97–118
DOI 10.4171/DM/98