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Split-octonion

In mathematics, the split-octonions are an 8-dimensional nonassociative algebra over the real numbers. Unlike the standard octonions, they contain non-zero elements which are non-invertible. Also the signatures of their quadratic forms differ: the split-octonions have a split signature (4,4) whereas the octonions have a positive-definite signature (8,0).

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Overview

Definition

Properties

Zorn's vector-matrix algebra

Applications

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Map overview Semantic statistics

Split-octonion

Nodes42
Edges41
Triples25
Avg. degree1.95
Density0.047619
Components1

How this topic connects Entity context

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Split-octonion

Top relations

has application · 8
Split-octonion → For, G2, Split-octonions, SU, Supersymmetric, The, The Dirac, The Zorn-based
related to Properties · 6
Split-octonion → Also, Artin's, Moufang, That, The, Therefore
related to Zorn's vector-matrix algebra · 5
Split-octonion → Define, R3, Since, Specifically, Zorn
related to Cayley–Dickson construction · 4
Split-octonion → Cayley, Dickson, The, We
related to Conjugate, norm and inverse · 1
Split-octonion → The
related to Multiplication table · 1
Split-octonion → Every

Important terminology Word statistics

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Important terminology

split-octonions octonions form real algebra multiplication numbers algebras split given displaystyle elements quadratic octonion also nonassociative matrices composition defined 8-dimensional

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Split-octonionhas applicationSplit-octonions0.60section
Split-octonionhas applicationFor0.60section
Split-octonionhas applicationThe Dirac0.60section
Split-octonionhas applicationSupersymmetric0.60section
Split-octonionhas applicationThe Zorn-based0.60section
Split-octonionhas applicationSU0.60section
Split-octonionhas applicationThe0.60section
Split-octonionhas applicationG20.60section
Split-octonionrelated to Cayley–Dickson constructionThe0.60section
Split-octonionrelated to Cayley–Dickson constructionCayley0.60section
Split-octonionrelated to Cayley–Dickson constructionDickson0.60section
Split-octonionrelated to Cayley–Dickson constructionWe0.60section

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