SO(10,C)

URI: https://gptkb.org/entity/SO(10,C)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:Lie_group
gptkbp:automorphismGroup	gptkb:SO(10,C)
gptkbp:centralTo	gptkb:Z/2Z
gptkbp:compact	true
gptkbp:complexification	gptkb:SO(10)
gptkbp:connects	true
gptkbp:dimensions	45
gptkbp:field	complex numbers
gptkbp:fullName	gptkb:Special_Orthogonal_Group_in_10_dimensions_over_the_complex_numbers
gptkbp:fundamentalGroup	gptkb:Z/2Z
gptkbp:groupOrder	infinite
gptkbp:hasConnection	true
gptkbp:hasMaximalTorus	(C^*)^5
gptkbp:hasSubgroup	gptkb:GL(10,C)
https://www.w3.org/2000/01/rdf-schema#label	SO(10,C)
gptkbp:isAlgebraicGroup	true
gptkbp:isClassicalGroup	true
gptkbp:isMatrixGroup	true
gptkbp:isQuotientOf	gptkb:Spin(10,C)
gptkbp:isReductive	true
gptkbp:isSemisimple	true
gptkbp:isSimple	true
gptkbp:Lie_algebra	so(10,C)
gptkbp:maximalCompactSubgroup	gptkb:SO(10)
gptkbp:notation	gptkb:SO(10,ℂ) gptkb:SO(10,C)
gptkbp:rank	5
gptkbp:realForm	gptkb:SO(10,R)
gptkbp:relatedTo	gptkb:Spin(10,C) gptkb:Dynkin_diagram_D5 gptkb:SO(10,R) gptkb:Lie_group quadratic forms Cartan subalgebra orthogonal group spinor representation orthogonal geometry
gptkbp:simplyConnectedCover	gptkb:Spin(10,C)
gptkbp:type	gptkb:group_of_people gptkb:Lie_group gptkb:D5
gptkbp:usedIn	gptkb:theoretical_physics representation theory grand unified theories
gptkbp:Weyl_group	gptkb:Weyl_group_of_type_D5
gptkbp:bfsParent	gptkb:SO(10)
gptkbp:bfsLayer	6