general linear groups

GPTKB entity

Statements (23)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:abbreviation gptkb:GL(n,_F)
gptkbp:actsOn vector spaces
gptkbp:centralTo scalar matrices
gptkbp:contains identity matrix
gptkbp:defines group of invertible n×n matrices over a field F
gptkbp:field group theory
linear algebra
gptkbp:hasSubgroup gptkb:orthogonal_group
gptkbp:heldBy gptkb:algebraic_geometry
non-abelian for n > 1
Lie group when F = R or C
gptkbp:importantFor gptkb:algebraic_geometry
number theory
representation theory
gptkbp:isQuotientOf gptkb:projective_general_linear_group
gptkbp:notation gptkb:GL(n,_F)
gptkbp:operator matrix multiplication
gptkbp:order (q^n-1)(q^n-q)...(q^n-q^{n-1}) for GL(n, F_q)
gptkbp:relatedTo automorphism group of vector space
gptkbp:bfsParent gptkb:Deligne_category
gptkbp:bfsLayer 8
https://www.w3.org/2000/01/rdf-schema#label general linear groups