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

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Quéguiner-Mathieu, Anne [Université Paris 13] Garibaldi, R. Skip [University of California Los Angeles] Tignol, Jean-Pierre [UCL]

For A a central simple algebra of degree 2n, the n-th exterior power algebra λ^nA is endowed with an involution which provides an interesting invariant of A. In the case where A is isomorphic to Q ⊗ 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.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2001
Language Anglais
Journal information "Documenta Mathematica" - Vol. 6, no. 1, p. 97-118 (2001)
Peer reviewed yes
Publisher Deutsche Mathematiker Vereinigung ((Germany) [S.l.] )
issn 1431-0635
Publication status Publié
Affiliations Université Paris 13 - LAGA
University of California Los Angeles - Department of Mathematics
UCL - SC/MATH - Département de mathématique
Keywords Trace forms ; Involutions ; Central simple algebras
Links
Bibliographic reference Quéguiner-Mathieu, Anne ; Garibaldi, R. Skip ; Tignol, Jean-Pierre. Involutions and Trace Forms on Exterior Powers of a Central Simple Algebra. In: Documenta Mathematica, Vol. 6, no. 1, p. 97-118 (2001)
Permanent URL http://hdl.handle.net/2078.1/79985