The isometry classification of Hermitian forms over division algebras

DOI10.1016/0024-3795(82)90258-0zbMath0488.10020OpenAlexW2025371642MaRDI QIDQ1165885

David W. Lewis

Publication date: 1982

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(82)90258-0

zbMATH Keywords

surveybibliographyquadratic formsisometry classificationepsilon-hermitian forms over division algebras with involutionepsilon-symmetric bilinear forms over fieldsskew-hermitian forms over quaternion algebra

Mathematics Subject Classification ID

Quadratic forms over general fields (11E04) Hermitian, skew-Hermitian, and related matrices (15B57) General binary quadratic forms (11E16)

Related Items (7)

Unnamed Item ⋮ The Apollonian structure of Bianchi groups ⋮ Algebraic characterization of isometries of the complex and the quaternionic hyperbolic planes ⋮ A finiteness theorem for special unitary groups of quaternionic skew-Hermitian forms with good reduction ⋮ Signatures of Hermitian forms and the Knebusch trace formula ⋮ The Hasse principle for similarity of Hermitian forms ⋮ Infinite-dimensional groups over finite fields and Hall-Littlewood symmetric functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The equation \(\bar t at=b\) in a quaternion algebra
• Classification theorems for quadratic forms over fields
• Hermitian forms. II
• Zur Klassifikation schiefhermitescher Formen über Zahlkörpern. (On the classification of skew Hermitean forms over number fields)
• Invarianten hermitescher Formen über Schiefkörpern. (Invariant Hermitean forms over skew fields)
• Cohomologische Invarianten quadratischer Formen
• Quadratic forms over nonformally real fields with a finite number of quaternion algebras
• Forms over real algebras and the multisignature of a manifold
• The equivalence of sesquilinear forms
• Quadratic forms in infinite dimensional vector spaces
• Quadratic and Hermitian forms in additive and Abelian categories
• On some Hasse principles over formally real fields
• The equivalence of bilinear forms
• Clifford algebras for algebras with involution of Type D
• Formes quadratiques, groupes orthogonaux et algèbres de Clifford
• Quadratic forms and Galois cohomology
• On isometries of inner product spaces
• Klassifikation hermitescher Formen über lokalen Körpern
• Algebraic \(K\)-theory and quadratic forms. With an appendix by J. Tate
• On the local theory of quaternionic anti-hermitian forms
• Symmetric bilinear forms and quadratic forms
• On the classification of Hermitian forms. II: Semisimple rings
• Lectures on Galois cohomology of classical groups. With an appendix by T. Springer
• Forms over rings with involution
• Quadratic forms
• The square class invariant for quadratic forms and the classification problem
• Hermitian Forms I
• Similarity of Quadratic Forms and Isomorphism of Their Function Fields
• Generic Splitting of Quadratic Forms, I
• Generic Splitting of Quadratic Forms, II
• Prospects in Mathematics. (AM-70)
• Quadratic Forms Over Formally Real Fields and Pythagorean Fields
• On the conjugacy classes in the unitary, symplectic and orthogonal groups
• Hermitian quadratic forms in a quasi-field
• Quadratic forms over arbitrary fields
• Pairs of quadratic forms
• Quadratic forms over arbitrary fields

This page was built for publication: The isometry classification of Hermitian forms over division algebras