A Cassels-Pfister theorem for involutions on central simple algebras

DOI10.1006/jabr.1996.0149zbMath0847.16019OpenAlexW2018679997MaRDI QIDQ1913983

Jean-Pierre E. Tignol

Publication date: 9 July 1996

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1996.0149

zbMATH Keywords

central simple algebrassymmetric elementshyperbolic involutionsCassels-Pfister Theorem

Mathematics Subject Classification ID

Quadratic forms over general fields (11E04) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Finite-dimensional division rings (16K20)

Related Items (12)

Cohomological invariants for orthogonal involutions on degree 8 algebras ⋮ Positive semidefinite univariate matrix polynomials ⋮ \(R\)-equivalence and rationality problem for semisimple adjoint classical algebraic groups ⋮ Algebras with involution that become hyperbolic under a given extension ⋮ Algebras with involution that become hyperbolic over the function field of a conic. ⋮ On quaternion algebras split by a given extension, Clifford algebras and hyperelliptic curves ⋮ An isomorphism problem for Azumaya algebras with involution over semilocal Bézout domains. ⋮ Hyperbolicity of algebras with involution over a given extension. ⋮ A Remark on Transfers and Hyperbolicity ⋮ A Generic Characterization of Direct Summands for Orthogonal Involutions ⋮ Hyperbolic Involutions and Quadratic Extensions ⋮ Hyperbolicity of certain involutions over the function field of a quadric

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