octonions

URI: https://gptkb.org/entity/octonions

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:algebra normed division algebra
gptkbp:alsoKnownAs	gptkb:Cayley_algebra gptkb:Cayley_numbers
gptkbp:alternative_algebra	true
gptkbp:basisFor	1, e1, e2, e3, e4, e5, e6, e7
gptkbp:contains	quaternions complex numbers real numbers
gptkbp:dimensions	8
gptkbp:discoveredBy	gptkb:Arthur_Cayley gptkb:John_T._Graves
gptkbp:discoveredIn	1843
gptkbp:divisionAlgebra	true
https://www.w3.org/2000/01/rdf-schema#label	octonions
gptkbp:identityElement	1
gptkbp:nonAssociative	true
gptkbp:nonCommutative	true
gptkbp:normedAlgebra	true
gptkbp:rank	real numbers
gptkbp:relatedTo	gptkb:Cayley–Dickson_construction gptkb:Bott_periodicity gptkb:sedenions gptkb:geometry gptkb:Spin(8) gptkb:Albert_algebra gptkb:exceptional_Jordan_algebra gptkb:Fano_plane gptkb:Hurwitz's_theorem gptkb:exceptional_Lie_algebras gptkb:G2_Lie_group gptkb:Moufang_loops gptkb:split-octonions gptkb:Clifford_algebras quaternions complex numbers real numbers division ring composition algebra nonassociative algebra triality
gptkbp:usedIn	gptkb:special_relativity gptkb:theoretical_physics gptkb:string_theory gptkb:exceptional_Lie_groups
gptkbp:zeroDivisors	false
gptkbp:bfsParent	gptkb:John_Horton_Conway gptkb:Grassmannian
gptkbp:bfsLayer	5