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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 29 April 1999
Rights and permissions
About this article
Cite this article
Lewis, D., Tignol, JP. & Parimala, R. Classification theorems for central simple algebras with involution (with an appendix by R. Parimala). manuscripta math. 100, 259–276 (1999). https://doi.org/10.1007/s002290050199
Issue Date:
DOI: https://doi.org/10.1007/s002290050199