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Classical group

In mathematics, the classical groups are the matrix groups arising from finite-dimensional vector spaces and from nondegenerate bilinear, sesquilinear, quadratic, and Hermitian forms. In the traditional setting of Lie groups, this includes the real, complex, and quaternionic general linear, special linear, orthogonal, unitary, and symplectic groups…

Measurement, Overview & Classical groups from central simple algebras with involution

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Overview

MathematicsNondegenerateBilinearSesquilinearQuadratic
29 related topics

Classical groups from central simple algebras with involution

Central simple algebraInvolutionQuadratic pairsÉtaleGroup schemes
8 related topics

Classical groups over arbitrary fields

Projective general linear groupProjective special linear groupSpinor normField extensionAlgebraic geometry
6 related topics

Groups preserving bilinear forms

Indefinite orthogonal groupSpecial orthogonal groupComplex orthogonal group
3 related topics

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Overview

Forms and automorphism groups

Groups preserving bilinear forms

Groups preserving sesquilinear forms

Quaternionic groups

Classical groups over arbitrary fields

Classical groups from central simple algebras with involution

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Classical group

Nodes58
Edges57
Triples70
Avg. degree1.97
Density0.034483
Components1

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Classical group

Top relations

related to References · 46
Classical group → An Introduction Through Linear, Artin, Basel, Berlin, Birkhäuser, Boston, Classical, Date, EMS PressRossmann, Encyclopedia, Ergebnisse, Geometric Algebra, Goodman, Graduate, Grenzgebiete, Groups, Heft, Hermann, III, Internet ArchiveDieudonné
related to Classical groups as algebraic groups · 5
Classical group → Dynkin, From, GL, In, The
related to Classical groups from central simple algebras with involution · 5
Classical group → Over, That, The, Thus, To
related to Examples over local fields · 3
Classical group → For, Thus, Typical
related to overview · 3
Classical group → For, In, Two
related to Classical groups over arbitrary fields · 2
Classical group → Lie, Over
related to Forms and automorphism groups · 2
Classical group → Let, The
related to Groups preserving forms · 2
Classical group → If, The
related to Quaternionic groups · 1
Classical group → For

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Important terminology

displaystyle groups classical group mathbb form mathrm algebra forms nondegenerate lie orthogonal bilinear involution quadratic unitary simple one linear hermitian

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
P S L ninstance ofThe classical families include groups0.80text
Classical grouprelated to Classical groups as algebraic groupsIn0.60section
Classical grouprelated to Classical groups as algebraic groupsGL0.60section
Classical grouprelated to Classical groups as algebraic groupsFrom0.60section
Classical grouprelated to Classical groups as algebraic groupsDynkin0.60section
Classical grouprelated to Classical groups as algebraic groupsThe0.60section
Classical grouprelated to Classical groups from central simple algebras with involutionThe0.60section
Classical grouprelated to Classical groups from central simple algebras with involutionThat0.60section
Classical grouprelated to Classical groups from central simple algebras with involutionTo0.60section
Classical grouprelated to Classical groups from central simple algebras with involutionOver0.60section
Classical grouprelated to Classical groups from central simple algebras with involutionThus0.60section
Classical grouprelated to Classical groups over arbitrary fieldsOver0.60section

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