Algebras of odd degree with involution, trace forms and dihedral extensions

DOI10.1007/BF02937309zbMath0871.16017OpenAlexW1977420418MaRDI QIDQ677414

Max-Albert Knus, Darrell E. Haile, Markus Rost, Jean-Pierre E. Tignol

Publication date: 28 May 1997

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02937309

zbMATH Keywords

central simple algebrassymmetric elementscohomological invariantsinvolutions of the second kind3-fold Pfister formscubic étale subalgebrasreduced tracessubfields with dihedral Galois groups

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)

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Structure Theorems for Jordan Algebras of Degree Three Over Fields of Arbitrary Characteristic ⋮ Galois cohomology of fields without roots of unity ⋮ Examples of algebraic groups of type \(G_2\) having the same maximal tori ⋮ Galois cohomology of special orthogonal groups ⋮ Local-global principle for classical groups over function fields of \(p\)-adic curves ⋮ On cubic étale algebras ⋮ A survey on Albert algebras ⋮ On cyclic twists of elliptic curves of period two or three and the determination of their relative Brauer groups ⋮ Invariants mod-2 and subgroups of \(G_2\) and \(F_4\) ⋮ Relative Brauer groups of genus 1 curves ⋮ All dihedral division algebras of degree five are cyclic ⋮ Zero cycles of degree one on principal homogeneous spaces ⋮ Cohomological Invariants of Central Simple Algebras with Involution ⋮ Embeddings of rank-2 tori in algebraic groups ⋮ Cohomological invariants of Jordan algebras with frames ⋮ Unitary \(\mathrm{SK}_1\) of semiramified graded and valued division algebras. ⋮ Open problems on central simple algebras. ⋮ Octonion algebras obtained from associative algebras with involution ⋮ Rational subgroups and invariants of \(F_4\) ⋮ Trialitarian automorphisms of Lie algebras. With an appendix by Knus and Larissa Cadorin. ⋮ Curves $\mathcal{C}$ that are cyclic twists of $Y^{2}=X^{3}+c$ and the relative Brauer groups $Br(k(\mathcal{C})/k)$ ⋮ More on rank-2 tori and its cohomological applications

Cites Work

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• The toral Tits process of Jordan algebras
• On division algebras of degree 3 with involution
• Cohomologie galoisienne. Cours au Collège de France, 1962--1963. Seconde édition.
• Algebraic \(K\)-theory and quadratic forms. With an appendix by J. Tate
• Pfister forms and \(K\)-theory of fields
• Forms in Odd Degree Extensions and Self-Dual Normal Bases
• Dihedral Algebras are Cyclic
• Nilpotence in the Witt Ring
• Cubic Subfields of Exceptional Simple Jordan Algebras
• Reduced models of Albert algebras