D.W. Lewis and J.-P. Tignol: Classification theorems for central simple algebras with involution, with an appendix by R. Parimala

david.lewis@ucd.ie, tignol@agel.ucl.ac.be

Submission: 1999, Apr. 21

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.

1991 Mathematics Subject Classification: 11E57, 16K20

Keywords and Phrases: algebras with involution

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