The trace form of a central simple algebra of degree 4.

DOI10.1016/j.crma.2005.11.002zbMath1110.16014OpenAlexW2058446170MaRDI QIDQ2583816

Jean-Pierre Serre, Markus Rost, Jean-Pierre E. Tignol

Publication date: 18 January 2006

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2005.11.002

zbMATH Keywords

quadratic formscentral simple algebrasquaternion algebrasnorm formssymbol algebrasWitt groupsPfister forms

Mathematics Subject Classification ID

Quadratic forms over general fields (11E04) Algebraic theory of quadratic forms; Witt groups and rings (11E81) Finite-dimensional division rings (16K20)

Related Items

Trialitarian triples, Faddeev invariants for central simple algebras over rational function fields, Cohomological invariants of central simple algebras of degree 4, Comparing invariants of \(\mathbf{SK}_1\), Degree four cohomological invariants for certain central simple algebras, Applications of the Bloch-Kato conjecture to cohomological invariants and symbol length, Cohomological Invariants of Central Simple Algebras with Involution, Central simple algebras of prime exponent and divided power operations, Open problems on central simple algebras., Cohomological operations for the Brauer group and Witt kernels of a quartic field extension, Division algebras over 𝐶₂- and 𝐶₃-fields, Essential dimension of central simple algebras., Biquaternion division algebras and fourth power-central elements, The second trace form of a central simple algebra of degree 4 of characteristic 2.

Cites Work

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• Cyclic and elementary abelian subfields of Malcev-Neumann division algebras
• Non-cyclic division algebras
• Kummer subfields of tame division algebras
• Generic construction of non-cyclic division algebras
• Division algebras over 𝐶₂- and 𝐶₃-fields