special linear group SL(3)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people gptkb:Lie_group
gptkbp:application	gptkb:algebraic_geometry differential geometry physics representation theory
gptkbp:centralTo	set of scalar matrices with cube roots of unity
gptkbp:connects	yes (over complex or real numbers)
gptkbp:defines	group of 3x3 matrices with determinant 1
gptkbp:dimensions	8
gptkbp:field	general field
gptkbp:generation	elementary matrices
gptkbp:hasSubgroup	general linear group GL(3)
https://www.w3.org/2000/01/rdf-schema#label	special linear group SL(3)
gptkbp:identityElement	3x3 identity matrix
gptkbp:isNonAbelian	yes
gptkbp:isSimple	yes (for fields with more than 3 elements)
gptkbp:notation	SL(3) SL_3
gptkbp:operator	matrix multiplication
gptkbp:order	infinite
gptkbp:order_over_F_q	q^3(q^3-1)(q^2-1)
gptkbp:over_complex_numbers	gptkb:Lie_group
gptkbp:over_finite_field_F_q	gptkb:group_of_people
gptkbp:over_real_numbers	gptkb:Lie_group
gptkbp:rank	2
gptkbp:relatedTo	gptkb:special_linear_group_SL(n) projective special linear group PSL(3) special linear group SL(2) special linear group SL(4)
gptkbp:type	A2 (in Lie algebra classification)
gptkbp:bfsParent	gptkb:SO(3)
gptkbp:bfsLayer	7