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:associator	nonzero
gptkbp:automorphismGroup	gptkb:G2
gptkbp:basisFor	1, e1, e2, e3, e4, e5, e6, e7
gptkbp:category	gptkb:algebra gptkb:division non-associative algebra number system hypercomplex number
gptkbp:contains	quaternions complex numbers real numbers
gptkbp:dimensions	8
gptkbp:discoveredBy	gptkb:Arthur_Cayley gptkb:John_T._Graves
gptkbp:discoveredIn	1843
gptkbp:finite-dimensional	true
gptkbp:hasConjugation	true
gptkbp:hasNorm	true
https://www.w3.org/2000/01/rdf-schema#label	Octonions
gptkbp:identityElement	1
gptkbp:nonAssociative	true
gptkbp:nonCommutative	true
gptkbp:rank	real numbers
gptkbp:relatedTo	gptkb:Cayley–Dickson_construction gptkb:Bott_periodicity gptkb:sedenions gptkb:Moufang_loop gptkb:exceptional_Jordan_algebra gptkb:Fano_plane gptkb:Hurwitz's_theorem gptkb:exceptional_Lie_group_G2 gptkb:split-octonions gptkb:Clifford_algebras gptkb:Zorn's_vector-matrix_algebra triality projective plane over octonions
gptkbp:usedIn	gptkb:geometry gptkb:special_relativity gptkb:theoretical_physics gptkb:string_theory quantum logic
gptkbp:zeroDivisors	false
gptkbp:bfsParent	gptkb:Quaternions
gptkbp:bfsLayer	7