Classification theorems for central simple algebras with involution

Lewis, D. W. ; Tignol, J. -P. ; Parimala, R. (1999) Classification theorems for central simple algebras with involution Manuscripta Mathematica, 100 (3). pp. 259-276. ISSN 0025-2611

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Official URL: http://www.springerlink.com/content/r9fhealtjn88mx...

Related URL: http://dx.doi.org/10.1007/s002290050199

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

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