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Linear group

In mathematics, a matrix group is a group G consisting of invertible matrices over a specified field K, with the operation of matrix multiplication. A linear group is a group that is isomorphic to a matrix group (that is, admitting a faithful, finite-dimensional representation over K).

Standards, Classes of linear groups & Definition and basic examples

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Overview

Definition and basic examples

Classes of linear groups

Properties

Examples of non-linear groups

Representation theory

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Linear group

Nodes98
Edges97
Triples73
Avg. degree1.98
Density0.020408
Components1

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Linear group

Top relations

related to References · 27
Linear group → American Mathematical Society, An Elementary Introduction, An Introduction, Brian, Ergebnisse, Graduate Texts, Grenzgebiete, Hall, Infinite, ISBN, Lie Algebras, Lie Groups, Linear Groups, Mathematics, Mathematik, Matrix, Oxford Graduate Texts, Oxford University Press, Representations, Rossmann
related to Examples of non-linear groups · 23
Linear group → Again, By, By Burnside's, Finding, Fn, Grigorchuk's, Higman's, In, It, Lie, Neumann, Out, Since, Sp, Tarski, The, There, This, Thompson's, Thus
related to Properties · 7
Linear group → Burnside's, Finitely, In, Schur's, Selberg's, They, While
related to Finitely generated matrix groups · 6
Linear group → Arithmetic, Braid, For, On, The, While
related to Definition and basic examples · 5
Linear group → Basic, GLd, GLn, SLn, The
is a · 1
Linear group → group that is isomorphic to a matrix group

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Important terminology

linear group groups generated finitely example finite representation examples infinite lie matrices faithful theorem matrix field many class set classical

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Linear groupis agroup that is isomorphic to a matrix group0.90text
Grigorchuk's group are not linear.Again by the Tits alternativeinstance ofgroups of intermediate growth0.80text
as mentioned above all counterexamples to the von Neumann conjecture are not linearinstance ofgroups of intermediate growth0.80text
Tarski monster groups cannot be linear.There are examples of hyperbolic groups which are not linearinstance offinitely generated torsion groups0.80text
obtained as quotients of lattices in the Lie groups Spinstance offinitely generated torsion groups0.80text
Linear grouprelated to Definition and basic examplesGLd0.60section
Linear grouprelated to Definition and basic examplesBasic0.60section
Linear grouprelated to Definition and basic examplesThe0.60section
Linear grouprelated to Definition and basic examplesGLn0.60section
Linear grouprelated to Definition and basic examplesSLn0.60section
Linear grouprelated to Examples of non-linear groupsIt0.60section
Linear grouprelated to Examples of non-linear groupsZ/2Z0.60section

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