Classification theorems for central simple algebras with involution (with an appendix by R. Parimala) |
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Authors: | D. W. Lewis J.-P. Tignol R. Parimala |
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Affiliation: | Department of Mathematics, University College Dublin, Dublin, Ireland.?e-mail: david.lewis@ucd.ie, IE Institut de Mathématique Pure et Appliquée, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium. e-mail: tignol@agel.ucl.ac.be, BE Tata Institute of Fundamental Research, 400005 Bombay, India.?e-mail: parimala@math.tifr.res.in, IN
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Abstract: | The involutions in this paper are algebra anti-automorphisms of period two. Involutions on endomorphism algebras of finite-dimensional vector spaces are adjoint to symmetric or skew-symmetric bilinear forms, or to hermitian forms. Analogues of the classical invariants of quadratic forms (discriminant, Clifford algebra, signature) have been defined for arbitrary central simple algebras with involution. In this paper it is shown that over certain fields these invariants are sufficient to classify involutions up to conjugation. For algebras of low degree a classification is obtained over an arbitrary field. Received: 29 April 1999 |
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Keywords: | Mathematics Subject Classification (1991):11E39 16K20 |
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