Some applications of Jordan norms to involutorial simple associative algebras

DOI10.1016/0001-8708(83)90085-3zbMath0522.16030OpenAlexW1975004311MaRDI QIDQ1055865

Nathan Jacobson

Publication date: 1983

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(83)90085-3

zbMATH Keywords

central simple algebrasJordan algebrareduced normscentral simple algebras with involutiongeneric normgeneric norm fieldsgeneric splitting fieldsJordan norms

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Noncommutative Jordan algebras (17A15) Division rings and semisimple Artin rings (16Kxx)

Related Items (26)

Formes Quadratiques de Dimension 6 ⋮ Pfaffians and quadratic forms ⋮ A descent problem for quadratic forms ⋮ Cohomological invariants for central simple algebras of degree 8 and exponent 2 ⋮ Function fields of generalized brauer-severi varieties ⋮ A field of characteristic 2 withu-invariant 6 ⋮ Similarity of quadratic forms and related problems ⋮ The chain lemma for biquaternion algebras. ⋮ Certain properties of the tensor product of two Albert forms ⋮ Pfaffians, central simple algebras and similitudes ⋮ Degree four cohomological invariants for certain central simple algebras ⋮ Generic Reducing Fields of Jordan Pairs ⋮ Cohomological Invariants of Central Simple Algebras with Involution ⋮ Anisotropic Forms of Higher Degree Under Finite Dimensional Field Extensions ⋮ Chain equivalences for symplectic bases, quadratic forms and tensor products of quaternion algebras ⋮ On the tensor product of composition algebras ⋮ Jacobson’s theorem for bilinear forms in characteristic 2 ⋮ The Witt ring kernel for a fourth degree field extension and related problems ⋮ Tensor Products of Composition Algebras, Albert Forms and Some Exceptional Simple Lie Algebras ⋮ Forms of the generic norm of a separable Jordan algebra ⋮ The Albert Quadratic Form for an Algebra of Degree Four ⋮ Biquaternion algebras and quartic extensions ⋮ Witt kernels and Brauer kernels for quartic extensions in characteristic two ⋮ Certain quadratic forms of dimension at most 6 and function fields of characteristic 2 ⋮ Isotropy of 8-dimensional quadratic forms over function fields of quadrics ⋮ Some projective varieties defined by Jordan algebras

Cites Work

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• Generic splitting fields of central simple algebras
• Norm polynomials and algebras
• Linear maps preserving reduced norms
• Structure groups and Lie algebras of Jordan algebras of symmetric elements of associative algebras with involution
• Symmetric bilinear forms and quadratic forms
• Lectures on quadratic Jordan algebras
• On the Galois cohomology of the projective linear group and its applications to the construction of generic splitting fields of algebras
• Über den Funktionenkörper der Normfläche einer zentral einfachen Algebra.
• On the Wedderburn norm condition for cyclic algebras
• Shorter Notes: A Simple Proof of a Theorem of Albert
• Tensor Products of Quaternion Algebras

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