Cohomological Invariants of Central Simple Algebras with Involution

DOI10.1007/978-1-4419-6211-9_8zbMath1260.11030OpenAlexW1693905580MaRDI QIDQ3001251

Jean-Pierre E. Tignol

Publication date: 31 May 2011

Published in: Quadratic Forms, Linear Algebraic Groups, and Cohomology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4419-6211-9_8

zbMATH Keywords

cohomology groupsinvariantsquadratic formsinvolutioncentral simple algebraWitt group (ring) of a field

Mathematics Subject Classification ID

Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Cohomology theory for linear algebraic groups (20G10) Finite-dimensional division rings (16K20) Galois cohomology of linear algebraic groups (11E72)

Related Items (3)

On totally decomposable algebras with involution in characteristic two. ⋮ Orthogonal involutions on central simple algebras and function fields of Severi-Brauer varieties ⋮ Degree 3 relative invariant for unitary involutions

Cites Work

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• Algebras of odd degree with involution, trace forms and dihedral extensions
• Cohomological invariants and \(R\)-triviality of adjoint classical groups.
• Quadratic forms of dimension 8 with trivial discriminant and Clifford algebra of index 4
• Cohomological invariants of quaternionic skew-hermitian forms
• Pfaffians, central simple algebras and similitudes
• A proof of the Pfister factor conjecture
• Galois cohomology of the classical groups over imperfect fields
• Discriminant of symplectic involutions
• Some applications of Jordan norms to involutorial simple associative algebras
• Cohomologische Invarianten quadratischer Formen
• Central simple algebras
• Classical groups and the Hasse principle.
• Similarity of quadratic forms and half-neighbors
• Galois Cohomology
• A note on trace forms and involutions of the first kind
• Cohomological invariants of algebras with involution
• Pfister involutions.
• On the Milnor conjectures: history, influence, applications.
• Classification theorems for central simple algebras with involution (with an appendix by R. Parimala)
• The discriminant of a symplectic involution.
• Arithmetic of linear algebraic groups over 2-dimensional geometric fields
• Lower \({\mathcal H}\)-cohomology of higher-dimensional quadrics
• Galois cohomology of the classical groups over fields of cohomological dimension \(\leq 2\)
• Signature of involutions of the second kind
• A criterion of decomposability for degree \(4\) algebras with unitary involution
• Clifford algebras for algebras with involution of Type D
• Formes quadratiques, groupes orthogonaux et algèbres de Clifford
• Isotropy of certain quadratic forms of dimensions 7 and 8 over the function field of a quadric
• The trace form of a central simple algebra of degree 4.
• Formes antihermitiennes devenant hyperboliques sur un corps de déploiement
• Algebraic groups with few subgroups
• Cohomological invariants of odd degree Jordan algebras
• Pfister’s theorem for orthogonal involutions of degree 12
• The Albert Quadratic Form for an Algebra of Degree Four
• Somme orthogonal d'algebres a involution et algebra de clifford
• APPLICATIONS OF CLIFFORD ALGEBRAS TO INVOLUTIONS AND QUADRATIC FORMS
• Représentations linéaires irréductibles d'un groupe réductif sur un corps quelconque.
• Orthogonal involution on algebras of degree 16 and the Killing form of E8
• On the signature of an involution
• Hermitian analogue of a theorem of Springer
• The Rost invariant has trivial kernel for quasi-split groups of low rank

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