R. Skip Garibaldi, Anne Quéguiner-Mathieu, and Jean-Pierre Tignol: Involutions and Trace Forms on Exterior Powers of a Central Simple Algebra

skip@member.ams.org, queguin@math.univ-paris13.fr, tignol@agel.ucl.ac.be

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

Full text: dvi.gz 33 k, dvi 84 k, ps.gz 192 k, pdf.gz 198 k, pdf 236 k.

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