special linear group SL(9)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people gptkb:Lie_group
gptkbp:application	gptkb:algebraic_geometry representation theory physics (symmetry groups)
gptkbp:centralTo	gptkb:cyclic_group_of_order_9_(when_over_complex_numbers)
gptkbp:connects	yes (over complex or real numbers)
gptkbp:defines	group of 9x9 matrices with determinant 1
gptkbp:dimensions	80
gptkbp:field	complex numbers (commonly used) real numbers (can be defined over any field)
gptkbp:generation	elementary matrices with determinant 1
gptkbp:hasSubgroup	gptkb:general_linear_group_GL(9)
https://www.w3.org/2000/01/rdf-schema#label	special linear group SL(9)
gptkbp:is_algebraic_group	yes
gptkbp:isNonAbelian	yes
gptkbp:isSimple	yes (for n>1, over algebraically closed fields except for small n)
gptkbp:notation	gptkb:SL(9) gptkb:SL_9
gptkbp:order	infinite
gptkbp:rank	8
gptkbp:relatedConcept	gptkb:projective_special_linear_group_PSL(9) gptkb:special_linear_Lie_algebra_sl(9)
gptkbp:type	classical group
gptkbp:bfsParent	gptkb:A_8
gptkbp:bfsLayer	7